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String theory and the crisis in particle physics

Bert Schroer

CBPF, Rua Dr. Xavier Sigaud 150

22290-180 Rio de Janeiro, Brazil

and Institut fuer Theoretische Physik der FU Berlin, Germany

December 2005

Abstract

In the first section the history of string theory starting from its S-matrix bootstrap predecessor up to Susskinds recent book is criticallyreviewed. The aim is to understand its amazing popularity which starklyconstrasts its fleeting physical content. A partial answer can be obtainedfrom the hegemonic ideological stance which some of its defenders useto present and defend it. The second section presents many argumentsshowing that the main tenet of string theory which culminated in thephrase that it represents the only game in town is untenable. It isbased on a wrong view about QFT being a mature theory which (apartfrom some missing details) already reached its closure.

1 An anthology of the crisis in fundamental physics

There can be no doubt that after almost a century of impressive success funda-mental physics is in the midst of a deep crisis. Although the epicenter of thequake which shakes its foundations is located in particle theory, its repercus-sions are not only beginning to derail experimental particle physics and to affectadjacent areas of fundamental research, but they are also leading to a weirdphilosophical fallout. One does not have to be a physicist in order to noticethat there is something strange going on if reputable people [1] are advocatingthe abdication of the kind of physics, which since the time of Galilei, Newton,Einstein and the protagonists of quantum theory has been a de-mystificationof nature by rational mathematically formulated concepts with experimentallyverifiable consequences. Instead of cogito ergo sum the new maxim is: I existand therefore my existence tells me what universe of the multiverses of solutionsof string theory I have to chose to understand my physical world. With otherwords I throw my own existence into the theory as a kind of boundary condition,or to put it more bluntly, I am integrating myself into string theory in order tomake it a work.

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One is used to view the exact sciences in particular particle physics as a hu-man activity which follows an intrinsic autonomous path. The resulting knowl-edge may have an impact on philosophy, the humanities and the developmentof society, but their feedback into fundamental research in physics is generallybelieved to be negligible. One of the points of this essay is to raise the questionwhether such a view can be maintained in a globalized world. Here I am notthinking primarily of the loss of moral standards in the increasing number offalsified or plagiarized scientific results. As long as the natural sciences main-tain the primate of verifiability this cannot derail its content. The danger ofderailment of particle physics is rather emanating from the hegemonic tenden-cies of monocultures which are pursued by globalized groups within science withan ever increasing unwillingness and inability to subject their results to criticalscrutiny. These developments have been looming in string theory for a longtime and finally found their explicit outing in a recent manifesto [1]. Before Ireturn to the question to what extend string theory and its new outing reflectsthe unpleasant side of the present Zeitgeist, it is helpful to review some relevantepisodes in the history of particle physics.

The beginning of relativistic particle theory is inexorably linked to JordansQuantelung der Wellenfelder which merged with Diracs multi-particle for-malism. QFT according to Jordan draws on a parallelism to classical fieldswhich amounted to a quantization of the classical canonical structure of theLagrangian formalism. Jordans point of view about this was more radical thanDiracs because any structure which fitted into the classical field formalism wasa potential candidate for quantization, it was not necessary that it belonged toreal observed classical physics1 as initially required by Dirac. In the light ofthis it is remarkable that two years after his discovery Jordan was dissatisfiedwith the use of what he called the classical crutches (klassische Kruecken)of quantization and pleaded for a more intrinsic access to the physical contentof QFT [3]. It is perhaps not accidental that this happened exactly at a timewhen he realized together with Pauli that the pointlike nature of quantum fieldsrequired by quantization are (unlike quantum mechanical observables) necessar-ily rather unwieldy singular objects which could lead to trouble in building upinteractions by their local couplings. But Jordans dream of an intrinsic andmore autonomous approach remained unfulfilled for a long time to come, thehistory of QFT between the early 1930s and the late 40s is characterized byapparently incurable ultraviolet problems. This ultraviolet crisis led to manyspeculative and revolutionary ideas (some of them quite weird, at least inretrospect). As a result of the Tomonaga-Schwinger-Feynman-Dyson renormal-ized perturbation theory and its immediate physical success in QED, these ideaswent into the dustbin of history.

Despite a formidable technical and conceptual enrichment, renormalizationwas extremely conservative in terms of physical principles; it was not necessaryto introduce a single physical principle beyond the ones which were already

1In [2] it is mentioned that by the time the Goettinger group learned about Schroedingersresults, Jordan already had a field quantized version.

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(indirectly or directly) in place in the pre-renormalization setting. But with-out renormalization theory and its successful application to QED, quantum fieldtheory probably would not have been able to survive in the pantheon of physics.However Jordans plea for intrinsicness was not laid to rest; rather perturbativerenormalization elevated it to a higher level. Instead of the pre-renormalizationultraviolet problem there was the new problem which consisted in the realiza-tion that the perturbative division into non-renormalizable and renormalizablemodels was rather technical; it was based on a formal quantization procedurewhich required the implementation of interactions by the recipe of couplingpointlike free fields rather than by letting the principles which underlie QFTdetermine an intrinsic way. Hence it is not possible to decide if and how thisformal division into renormalizable and nonrenormalizable models is related tothe genuine intrinsic frontier between well- and ill- defined theories. What com-plicates the situation is the fact that one could not even decide whether thereasonably looking renormalizable family really corresponds to models whichexist in any mathematical sense so that one at least would know that the prin-ciples allow for nontrivial realizations. The problem that particle physics mostsuccessful theory of QED is also its mathematically most fragile has not goneaway. These problems become even worse in theories as string theory which inthe eyes of string protagonists are supposed to supersede QFT. In this case onehas in addition to the existence problem the conceptual difficulty of not havingbeen able to extract characterizing principles from ad hoc recipes.

Even though renormalization theory (despite its crucial role in arriving ata new ultraviolet-controlled computational setting) did not really add a newphysical principle, its covariant formulation was instrumental for a profoundunderstanding of the particle-field relation. It replaced the relativistic quan-tum mechanical setting (the basis of the older textbooks of Wenzel and Heitler)which turned out to be unsuitable for this task2. In the new setting it was possi-ble to derive a large-time asymptotic relation which illuminated the connectionbetween particles and fields without invoking perturbation theory; the resultingLSZ scattering theory was shown to be a direct consequence of the principles[4]. The upshot of this conceptual progress was that asymptotic particle statesand the scattering matrix had the status of truly intrinsic quantities, whereasquantum fields (apart from symmetry-generating currents) loose the aspect ofindividuality which they enjoyed in classical physics before quantization; in factthere are infinitely many ways of choosing field coordinatizations and they canbe grouped into local equivalence classes of which every (interpolating) mem-ber field is describing the same particles whose charge numbers and spacetimerepresentation invariants (mass, spin) are related to the class (i.e. the particlestate is uniquely related to the class and not to the field). The deepening of thefield-particle relation led also to the revival of an idea by Heisenberg (which inits original form was discussed at some conferences shortly before the start of

2The quantum mechanical view of the particle-field relation became problematic after Furryand Oppenheimer observed that the presence of interactions made it impossible to obtain aspace-time separation of one field states A(x) |0 into a one particle states and their vacuumpolarization companions.

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the second world war) to explore the feasibility of a direct S-matrix construc-tion without passing through a field theory setting; in this way one expectedto obtain a non-singular and more intrinsic way to pursue particle physics. Forlack of a clear implementing strategy letting alone concrete results the interestwaned and only reappeared in the 1950s and 1960s in connection with some non-perturbative conceptual advances in the wake of renormalization theory (whichwere mainly driven by the issue to make QFT fit for describing strong inter-actions). On the one hand the adaptation of the Kramers-Kronig dispersionrelation to relativistic particle scattering and the related more general interestin analytic properties of scattering amplitudes and (electromagnetic) formfac-tors nourished the (exaggerated hope, as it turned out later) hope that manydynamical aspects could perhaps be understood as consistency relations be-tween analytic properties and reasonable assumptions about asymptotic high-and low-energy (threshold) behavior. Initially the aims of these investigationswere quite modest in that particle physicists were already satisfied when theysucceeded to derive experimentally verifiable sum rules from current commuta-tion relations and analytic properties (the prototype being the Thomas-Kuhnsum rules which played an important role in the transition from old to new QT).

The most important post-Heisenberg conceptual enrichment of S-matrix the-ory (coming originally from Feynmans graphical formulation of renormalizedperturbation theory) was however the crossing property often called (by abuseof language) crossing symmetry. Its off-shell version is a formal property whichrelates scattering graphs with other ones obtained by crossing pairs of externallines in incoming and outgoing configurations; in certain cases it could be ver-ified outside perturbation theory by studying axiomatically derived analyticbehavior following from locality and positivity of energy. For on-shell quan-tities as scattering amplitudes or formfactors of currents such derivations (forthose configurations for which they were possible) were quite demanding; oftenon-shell crossing properties were simply postulated in order to explore their ob-servable consequences, leaving their derivation from the causality and spectralprinciples of QFT to future progress. It is of course standard practice to useinteresting properties as working hypothesis, even if one is not yet in the posses-sion of a conceptual derivation3 from known principles; the only problem withthat is that after the passing of time, even with better conceptual insights andmathematical tools available, one may have forgotten about their problematicstatus.

The emerging so-called S-matrix bootstrap program, which owed its sec-ond life (after Heisenbergs first attempt) to the important but incompletelyunderstood crossing property, was on top of the physical fashions of the late50s and maintained its leading role through the 60s. Some of its points werequite reasonable; but the human weakness of making exaggerated promises (atheory of everything except gravity), and finally the strong return of QFT inthe form of nonabelian gauge theories, led to its demise. Among the few valu-

3The conjecture that on-shell crossing is a relic left by spacelike (anti)commutativity isplausible but there exists up this date no mathematical derivation (see remarks in next sec-tion).

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able points it contributed is the attention it drew to the fact that an on-shellapproach (if it succeeds) is not only free of ultraviolet problems but it is alsomanifestly independent of the infinite number of possibilities for pointlike fieldcoordinatizations (leading all to the same physics); in this sense it addressed,together with the independently emerging algebraic QFT during the 60s, forthe first time Jordans plea for intrinsicness of the description (abandonment ofclassical crutches).

The emphasis on an intrinsic description is well known in mathematics; itunderlies the invariant description of modern differential geometry which notonly liberated geometry from the use of singular coordinates, but from the useof any coordinatization altogether. This should be understood as nothing morethan an analogy, i.e. the use of modern differential geometry in the formulationof QFT does not make the latter more intrinsic; in fact the implementation ofintrinsicness in QFT turns out to be a much more radical step than in differ-ential geometry. But the antagonistic bellicose tone in which the underlyingbootstrap philosophy was set against QFT (QFT is like a mortally woundedsoldier dying on the battlefield...) undermined its credibility in the eyes ofmany physicists, and in my opinion, looking at this situation in retrospect, thisdelayed an interesting chance to enrich QFT by adding a new viewpoint for sev-eral decades (see next section); only now, as a result of the crisis, the situationforces young physicists who are out to re-capture the lost path of innovationsto revisit the relics on the wayside of the great caravan of particle physics (formore details see [5]).

Since there was no operator formalism in which the underlying ideas (invari-ance, unitarity, crossing, maximal analyticity) could be implemented, the prob-lem of constructing a crossing symmetric unitary maximally analytic S-matrixwas ill-formulated. Tinkering with properties of Beta functions and their repre-sentation in terms of Gamma functions, Veneziano was able to construct the firstmodel for a crossing symmetric elastic scattering amplitude. His proposal didnot satisfy unitarity, but the realization that his on-shell prescription allowedan auxiliary field theoretic description in terms of a (off-shell) two-dimensionalconformal field operators theory and that it also admitted an auxiliary presenta-tion in terms of the canonical quantization of a classical relativistic Nambu-Gotostring Lagrangian contributed significantly to its theoretical attraction. It alsonourished the hope that the model can be unitarized in a later stage. Its mainpopularity it however enjoyed among strong interaction phenomenologists whoactually (for reasons which nowadays hardly anybody remembers) liked the ideaof satisfying crossing already with infinite towers of intermediate particle states(duality = one-particle crossing) without the participation of the multi-particlescattering continua as would be required for an S-matrix coming from QFT. Inconjunction with the phenomenological use of ideas of Regge poles the emerg-ing trajectory pictures (mass versus spin) had a certain phenomenological charm(and probably were Venezianos physical motivation), and although infinite par-ticle towers cause some field theoretic headache4, there was no reason to reject

4Unless only a finite number of particles remain as stable objects (and infinitely many are

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it as a phenomenological proposal which captures some aspects of strong inter-actions. and whose possible relation with the known principles could be clarifiedafter establishing some phenomenological success.

The subject became somewhat problematic when the phenomenological in-terpretation in terms of Regge trajectories for strongly interacting scatteringamplitudes was abandoned (partially because the description of high transversemomentum scattering data worsened) and a new gravitational interpretation onthe level of the Planck scale was proposed (the Bartholomew day massacreof the old dual model string theory by J. Scherk et.al. 1975 in Paris). Thenew message was the suggestion that string theory (as a result of the presenceof spin two and the apparent absence of perturbative ultraviolet divergencies)should be given the status of a fundamental theory at an energy scale of thegravitational Planck mass 1019GeV i.e. as a true theory of everything (TOE),this time including gravity. Keeping in mind that the frontiers of fundamentaltheoretical physics (and in particular of particle physics) are by their very na-ture a quite speculative subject, one should not be surprised about the highlyspeculative radical aspects of this proposals; we know from history that someof our most successful theories originated in a similar manner. What is wor-risome about this episode is not so much its speculative nature but rather itsuncritical reception. After all there is no precedent in the history of physics ofa phenomenologically conceived idea for laboratory energies to became mirac-ulously transmuted into a theory of everything by just sliding the energy scaleupward through 15 orders of magnitudes and changing the terminology withouta change in its mathematical-conceptual setting5.

One would have expected that a speculative idea which has lost its phe-nomenological support basis and instead jumped into a conceptual blue yon-der beyond the range of QFT would receive at least that amount of criticalattention with which particle theorists analyzed previous situations of appar-ent conceptual conflicts from new proposals with established principles. Afterall antinomies and paradoxical situations were the source of great conceptualadvances in the last century; often the results obtained from their resolutionwere more important than the original idea by itself. Unfortunately this is notwhat happened in the case of string theory. The times of critical spirits ofthe caliber of Pauli had long passed and the new love affair between physicistsand mathematicians which left its mark in the great Atiyah-Witten dialoguewas more directed towards finding beauty and harmony (between differentialgeometry and topology on the one side with the artistry of the Euclidean func-tional integral on the QFT side) than to the task of carrying antinomies betweenknown structures of local quantum physics and new speculative ideas to theirbreaking point. The enthusiasm about a new golden age between mathemat-ics and theoretical particle physics was mutual, but I think it was based on adeep misunderstanding. Physicists were impressed by depth of modern coordi-

converted to poles in the second Riemann sheet) one gets into trouble with locality (this canbe seen in the context of d=1+1 factorizing theories).

5Some geometrical enrichments came much later and did not really modify the core of thesituation.

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natization free differential geometry and topology and started to write articlesin which they explained to their fellow physicists what they have learned andhow it can be used for the quasiclassical exploration of functional integrals6.On the other hand mathematicians were impressed by the geometrical powerof some computational tools of physicists. They begun to look in awe at theEuclidean functional integrals7; fortunately for mathematics they often foundrigorous ways to confirm conjectures suggested by these formal tools of thephysicists. Only very few mathematicians (including Vaughn Jones) were ac-tually aware that some of their colleagues were erecting their beautiful edificeson some of the ruins of particle physics. The interesting geometrical content ofstring theory contributed to the rather uncritical support it received even fromreputable people. This in my view was the historical beginning of a mode offree-floating discursive thinking which finally after almost 3 decades led to theabdication of what used to be fundamental physics. As already mentioned thiserosion process had its recent outing in a semipopular anthropic manifesto byL. Susskind.

Before looking more closely to the sociological changes which came with theincreasing popularity of string theory, it is quite instructive to analyse the ori-gin of its somewhat confusing terminology. The historical reason why the namedual model (after its interpretative paradigmatic change which allegedly in-corporates gravity) was converted to string theory had nothing to do with itsquantum localization in space time but refers to the infinite particle towermass spectrum which the canonical quantization of a free classical relativisticstring leads to; the intrinsic quantum localization of e.g. a canonical quan-tized Nambu-Goto string is despite its classical origin not string-like but ratherpointlike (more on this see below and next section), a first indication that thecherished quantization parallelism between classical and quantum localizationis limited to pointlike objects. In particular those Euclidean tube pictures can-not be interpreted as the time-development of physically string-like localizedobjects. One may justifiably fear that this could create a conceptual salad inthe minds of newcomers unless they are especially warned that the terminologyshould not be confused with the physical content. Its more recent descendantcannot create this kind of confusion since it receives its name M-theory justfrom the alphabet of big Latin letters, but far from this being a precautionarymeasure for not prejudicing its frail content, one is invited (according to Wit-

6The euclidean functional integral representation as well as the closely related canonicalquantization are formal artistic devices which acquire a mathematical meaning in the quasi-classical interpretation; renormalized correlation functions in strictly renormalizable theoriesare however not representable in this manner (only their meaningless unrenormalized analogsare formally consistent with functional integral representations).

7This deepened already existing misunderstandings between the concept of localization(the living space) of a theory and its Bargmann-Wightman-Hall analyticity region and ledto such confusing terminology as chiral QFT on Riemann surfaces. It also led to statementsthat their symmetry group is the group of analytic maps (only in [6] a mathematician pointsout that this does not define a group and wonders what physicists could possibly mean bythis; in order to resign with the statement that in view of the interesting results they must bein the pocession of a correct meaning) instead of the group of diffeomorphisms of the circle.

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ten) to interpret M among other things as standing for mystery (also matrix,mother, magic, in short a true theory of everything). Interpretation like thisfacilitates my attempts in this essay to describe string theory a la Susskindas a return to scholastic pre-Galilei-Newton-Einstein re-mystification of nature,which attaches weight to the question of how many vacua fit onto a universalstring (alias how many angels fit onto the pin of a needle).

In this essay I will argue that this crisis cannot really be understood in termsof physics without taking into account sociological changes of the increasinglyglobalized community of physicists who is pursuing this kind ideas. My experi-ence with string theoreticians is admittedly marked by a certain distance sincemy underlying philosophy has basically remained a bit more Wilsonian in thesense that reality in my view consists of an infinitely many shells of asymptot-ically inclusive theories (like the sheets of a possibly infinite onion). Perhapssomewhat different from Ken Wilson (I do not know his opinion on this point),I believe that every shell can be described in conceptually complete and math-ematically rigorous way, i.e. mathematical consistency alone does not requireknowledge of the next layer (the unreasonable efficiency of mathematics in thesense of Wigner). In fact the attempt to dump the details of the next layer intoa cutoff parameter could mathematically be even counterproductive8. In otherwords I believe that the 70 year old weakness of not knowing whether thoseobjects we talk about in QFT really exist still will be overcome, in fact I think(see remarks in the next section) that the day when QFT will enjoy the sameconceptual status as other areas of physics is not very far; but for the time beingQFT did not reach closure.

I do not subscribe to the underlying idea of string theory that a TOE is at allpossible. In fact the idea that Einsteins Dear Lord (the one who does not throwdice) permits some string theorist to find a closure to fundamental physics (sothat for the rest of all days the curiosity of humanity about its material world willend in intellectual boredom or at best re-directed into a plumbing job for some ofthe still missing details or perhaps subsumed into a branch of the entertainmentindustry) appears to me outright ridiculous. Ideas like this probably will becited by historians in a distant future as representing the hubris and intellectual(not necessarily personal) arrogance of a past Zeitgeist. The best one can do toillustrate these points is to quote statements from string theorists. One citationby which an apparently reputable young (but apparently very immature) stringtheorist9 used to sign off his contributions to discussion groups reads as follows[7]:

Superstring/M-theory is the language in which God wrote the world.Whenever I looked at that line (I stopped looking 3 years ago, hence I do

not know whether dictums like this still enjoys popularity) an old limerick cameto my mind. It originates from pre-war multi-cultural Prague where, after aperformance of Wagners Tristan and Isolde by a maestro named Motl, an art

8Note that string theory, if anything, has a much worse existence problem; it is not evenpossible to give an intrinsic characterization, the only thing one has are cooking recipes.

9As in the religious domain there is of course the risk of violating somebodies feeling. Butwithout using the freedom of expression this essay would lack substance and credibility.

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critic wrote instead of the usual critical review in next days newspaper thefollowing limerick10 (unfortunately this cannot be translated from German toEnglish without a complete loss of charm):

Gehe nicht zu Motls Tristanschau Dir nicht dieses Trottels Mist an,schaff dir lieber nen drittel Most anund trink dir mit diesem Mittel Trost anWhat a difference of this God who has to follow the logic of string theory

(perhaps because there is no other game in town, see next section) to Ein-steins Dear Lord! Whom God allowed to have a copy of his blueprint of theworld does of course not have to bother about earthly worries of experimentalverifications; those remaining earthlings which are not in its possession, andwant to verify results of this divine theory in the old fashioned way by exper-iments and observations will have no chance since they never can get to therequired energy scale. Even a theoretical comparison with existing principlesof quantum field theory is not possible, because string theory is only known interms of recipes which have resisted an intrinsic characterization by principles.This situation is without precedent in the history of physics.

String theorists offer their well known scale-sliding arguments to show thatLagrangian field theory is a low energy footnote of string theory. But thosearguments are no substitute for a structural comparison. To illustrate what ismeant by structural consider the somewhat analogous relation between QMand QFT. The structural reason is that there exist relativistic field operatorswhich in their one-time application to the vacuum create one particle stateswithout any admixture of vacuum polarization. These are the free Bose/Fermifields. If we would live in a (d=1+2) world of anyons and plektons (particles withbraid-group statistics) the nonrelativistic version would not be QM but rathera quantum field theory11 with a nonrelativistic dispersion law. The relevanceof QM to the physical world is related to the fact that particle number conser-vation is compatible with the relativistic spin-statistics connections of Bosonsand Fermions. It has not been possible to make such structural arguments instring theory because recipes are no substitute for principles and the fact thatone knows a lot about the principles which characterize QFT is of no help here.

For readers who want to see string-theoretic adulation in its purest form, Irecommend the article in [8] where one finds the following passage:

In the 1990s, Edward Witten and others found strong evidence that the dif-ferent superstring theories were different limits of an unknown 11-dimensional

10I am indepted to a reader for pointing out to me that the viertel in my original versionshould be replaced by drittel. I appologize for having caused this temporary distortionof the most perfect example of a German Schuettelreim (spoonerism), but the old measure(Schoppen=1/3) has not been used any longer during my wining years; nowadays it is 1/4.

11Wilszeks quantum mechanical anyons (Aharonov-Bohm like dyons) violate the spin statis-tic relation for an anomalous value of the spin; one consequence of this violation is that thatthe resulting multi-dyon QM does not permit a description in the second quantization Fockspace setting. True anyons however remain field theoretical for all energies and never loosetheir vaccum polarization clouds (even in the absence of genuine interactions). A formalscale-sliding argument could easily overlook this subtle structural point.

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theory called M-theory. These discoveries sparked the second superstring rev-olution. When Witten named M-theory, he didnt specify what the M stoodfor, presumably because he didnt feel he had the right to name a theory whichhe hadnt been able to fully describe. Guessing what the M stands for has be-come a kind of game among theoretical physicists. The M sometimes is saidto stand for Mystery, or Magic, or Mother. More serious suggestions includeMatrix or Membrane. Sheldon Glashow has noted that the M might be anupside down W, standing for Witten. Others have suggested that the Min M-theory should stand for Missing, Monstrous or even Murky. Accordingto Witten himself, as quoted in the PBS documentary based on Brian GreenesThe Elegant Universe, the M in M-theory stands for magic, mystery, ormatrix according to taste.

With such statements of scholastic adulation and a dash of talk-show en-tertainment12, one is almost inclined to consider the first phrase of this article:String theory is a model of fundamental physics whose building blocks are one-dimensional extended objects (strings) rather than the zero-dimensional points(particles) i.e. the standard opening mantra used by string theorists, as a light-hearted lapsus linguae rather than a potential source of misconception. It wasalready mentioned before that whereas it is true that the extension of the clas-sical Nambu-Goto string (whose canonically quantized version is the motherof the string-theoretic reformulation of Venezianos dual model) is really a rela-tivistic spacetime string, this is not the case for its canonically quantized coun-terparts. The only intrinsic notion of a quantum relativistic localization is thatobtained by translating this object into other positions and checking whetherits commutator with the original object is nonvanishing once the second wouldbe string shape enters the causal influence region of the first. Quantum lo-calization is an autonomous property and the case where it coincides with theclassical meaning is one of the greatest lucky coincidences and Jordan with hisfield quantization was very lucky indeed. This quantum localization test wasmade (even by string theorists) and the result was negative [9][10]; the commu-tator is just that of two pointlike objects localized at the center of mass pointsof the imagined strings. But the commutator test is lakmus test which decideswhether the use of the word string has an intrinsic quantum meaning. Thefact that string theory fails this test is not totally unexpected since the stringdescription is strictly auxiliary, it belongs to the classical side of the cookingrecipe for the construction of a particular crossing symmetric (and at the endhopefully unitary) S-matrix and it certainly does not have a similar conceptualphysical status as a generalization of the interpolating pointlike fields of the LSZscattering theory to a string-like Heisenberg field. Without the use of scatter-ing theory in terms of large timelike limits (of either point-like or semi-infinite

12The author of the Wikipedia article informed me that I misunderstood the intention ofhis remarks concerning the interpretation of M, the main purpose was to expose to his readersthe vagueness of the subject. But I am also a reader and a bit of irony or tongue in cheekin the phrasing would have helped me. If I am the only one who incorrectly interpreted thisas adulation through boastful mystification (that is at least the intention of Brian Green, ahumble admission of its speculative content would look different), I will retract my remarks.

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string-like localized interacting fields the relation of the S-matrix with localityis extremely indirect (and has been noticed only recently with the help of theconcept of modular localization for wedge regions [5], see also remarks in nextsection). Relativistic string-localized quantum objects which could substitutethe interpolating pointlike fields and those auxiliary constructs of string theo-rists are very different concepts. Our presently best knowledge about them maybe condensed into the statement: quantum string-localized objects (example thequantum fields behind the zero mass infinite spin Wigner representations) donot allow a representation in terms of Lagrangian quantization and on the otherhand the quantization of classical (Nambu-Goto type) strings does not lead toquantum string localization. This may at first sight come as a shock even to ordi-nary field theorists who expected the quantization approach (i.e. the invocationof a parallelism with classical structures) to be of general validity transcendingthe boundaries of pointlike localization. To contemplate a less singular moreintrinsic description without classical crutches, as Jordan did, is one thing,but to be confronted with a conceptual barrier which prevents to view certaina quantum object as a quantized version of a classical analog is a different andmore surprising issue. String theory is build on the supposition that geometricaspects and localization properties are maintained by quantization even if onegoes beyond pointlike fields.

There is another result, this time not referring to localization, which high-lights the strictly auxiliary nature of the meaning of the word string in stringtheory. It has been known that the Nambu-Goto string is an integrable sys-tem. The infinite family of conserved charges has been identified, and theirPoisson relations are known. One of the important messages coming in par-ticular from the early work of Faddeev on integrable systems that it is easierto arrive at the (nonperturbative) solution if one directly quantizes the closedsystem of algebraic Poisson-bracket solutions between the complete system ofconserved charges. But what should be done in a situation where the intrin-sic quantization of charges leads to results which disagree13 with the standardcanonical quantization as it is the case for N-G strings? [11]. The answer is:the dual model S-matrix construction requires the canonical quantization sincethe notion of string is just a short hand computational device for re-producingthe mass tower spectrum of the dual model, the question of what is the correctquantization of a physical N-G string may be interesting but is irrelevant in thepresent context since the string of string theory is only a computational trickto find a Lagrangian packing for the dual model with its infinite mass tower.With other words the second canonically quantized Nambu-Goto field theory isa special kind of infinite component theory

The above remarks should not be misunderstood as a plea for a morato-rium on speculative ideas. Particle physics needs in certain situations jumpsinto the blue yonder and the risk that they turn out to have no experimen-tal support and that their conceptual relation to established principles remains

13Among other things the invariant quantization of the N-G string does not distinguish anyparticular spacetime dimension.

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obscure has to be taken. The real worrisome aspect of string theory (and to alesser degree with supersymmetry) is not that it turned into a fashionable sub-ject without an observational basis or that it is unable to clarify its conceptualstatus with respect to the principles of QFT (which remains despite its incom-pleteness the best reference point); there were fashions before (the S-matrixbootstrap, Regge poles,...) which have attracted a lot of attentions and alsosuffered from the same shortcomings. But in the past there was enough criticalpotential to prevent such a condensation along a fashionable monoculture14.The situation has radically changed in that reputable and influential physicistswhose critical judgement could have a sobering impact on a confusing situationgive their uncritical support to these tendencies and in this way become partof the problem. Particle physics was at its best when physicists like Pauli whowere strongly committed to the truth were at the helm of particle physics. Thisled to a situation where contributions in this area are submitted to so calledhigh impact journals whose editorial board already consists of people who arehighly specialized on hot subjects (if not directly related to string theory, thenat least to its sociological fall-out) but are incapable (lack of background of ageneral physical culture) to evaluate anything else which does not follow theseglobalized lines15.

The main difference is that string theory (together and in union with super-symmetry) is the first theory which despite of these mentioned faults managedto survive for more than 3 decades. After such a long time the solid conceptualgrip on QFT which would be necessary to press ahead and carry string theoryto the breaking point in order to arrive at an enigmatic solutions of the pointsof structural tensions with QFT (or bury it, as it was done with several otherfailed theories before) is lost or (in case of younger string theorist) never existed.On the other hand those quantum field theorist who have this strength are notmotivated to look into the details of prescriptions for what they believe couldbe another failed theory; in addition they know that as a result of the sectarianideological attitude their critical remarks would not be welcome anyhow. Par-ticle physics in the past has successfully maintained its unity despite the useof widely different concepts and mathematical tools, but this unity is rapidlydissipating.

There is a related sociological problem. If an idea which promoted thecareers of many physicists is kept alive for such a long time it becomes immuneagainst criticism. I think nobody at this late point would seriously expect thatsomebody who invested more than 3 decades into a theory which led to tensof thousands of publications but failed to make contact with real physics willcome up and say sorry folks this was it!

14An beautiful example of a critical essay against some excrescences of the S-matrix boot-strap program and brilliant illustration of highly informative scientific polemicat its best onefinds in [12].

15But contrary to a normal referee who recognizes his limitations and sends it back to theeditor, this new breed rejects a paper without ever criticising its content, since in order to tomerit their attention they believe that you should belong to what they consider as their class(use their conceptual framework etc.).

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Theories which occupy minds for such a long time escape the critical radarscreen and develop a life of their own. Unfortunately there is no prior experiencewith similar problem in the past from which we could learn how to protect thecontent of fundamental physics against such new market tendencies. But even ifone does not know what to do about it, there is at least no problem to describethe situation in terms of the following 5 thesis:

1. Fundamental knowledge about particle theory and in particular aboutQFT has and is being lost.

2. The research in string theory is done and marketed by globalized groupswithout encountering an independent critical evaluation.

3. Newcomers to particle physics are prematurely exposed to highly specu-lative and controversial ideas before their critical immune system had achance to develop through a study of concepts of QFT.

4. String theorists dismiss the enigmatic power of antinomies and structuralclashes, papers which contain theorems which do not fit their prejudicesare simply ignored. The string theoretic literature consists mainly of cal-culations based on certain recipes and speculations, there is hardly anyattempt to provide a conceptual framework.

5. A large number of positions in particle theory have gone to string theorists.There are good reasons to worry that this could have negative long-lastingramifications for particle physics.

The case in favor of these statements is based on the following arguments.In talking to members of the younger generation of physicists one is often

surprised that they know very little about the great conceptual achievments ofthe 1950/60 post renormalization era. Although the recipes of the renormaliza-tion technology are usually part of their working knowledge (perhaps becauseit makes the string recipes more palatable), the conceptual achievments as thederivation of time-dependent scattering theory as a consequence of causality(LSZ, Haag-Ruelle) or the subtleties in the particle-field relation remain outsidetheir stock of knowledge. It seems that they have been replaced by differentialgeometry (often only in a Euclidean setting), and such special ideas as the pos-sible use of Calabi-Yau manifolds in particle physics. One does not have to beold-fashioned in order to be concerned about such trends.

Unfortunately those QFT textbooks which have been written by veterans ofstring theory emphasize this cooking book recipe approach to QFT. Why shouldsomebody to whom the S-matrix is nothing but the result of a string theorycooking recipe mention the (profoundly beautiful) result of scattering theorybeing a consequence of spacetime causality and ensuing cluster properties? Thisis time consumimg and could be counterproductive for the marketing of stringtheory since it could undermine confidence in its recipes.

In order to illustrate the second point in the above list it is helpful to recallthat in earlier times there was a clear separation between the act of creation by

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the author and the critical evaluation of its content by his colleagues. Nowadaysauthors are often embedded in a globalized group and they communicate aninnovative idea among members of this group already before it could reach acertain amount of maturity. This has two consequences, on the one hand theidea becomes modified and its originally intended content may get diluted, andon the other hand the chance that the work receives a critical evaluation froman independent viewpoint is significantly reduced. The likely kind of criticismin such a setting is that of an ideological battle between two globalized groupsrather than a critical analysis of its content. Just imagine that Einsteins generalrelativity would have come into being within such a sociological environment.Imagine in particular that instead of struggling for years with his famous holeproblem and thinking it through by himself, he would have explained it to theother members of such a globalized group. The topic would have entered emailsand discussion groups and the result may have well been a total confusion formany years to come.

Another danger emanating from big groups whose interests is focussed onthe promotion of a particle physics monoculture is that they tend to controleditorial boards of so-called high impact journals and in this way prejudice theresearch topics of particle physics. The easiest way to obtain a list of who iswho in administrating the crisis of particle physics is to look at the editorialboard of a new electronic journal as JHEP (Journal of High Energy Physics).

The third point of the list is perhaps the most serious one. A theory whichhas in more than 30 years been unable to get its relation to physics straightenedout is presented to physics students as a theory of everything which super-sedes QFT before their critical faculties have been strengthened by learningabout the concepts and open problems of the most successful theory of par-ticle physics. To get an impression about the extend to which the bordersbetween education and indoctrination have been blurred already, it is instruc-tive to take a look an undergraduate course on string theory offered at MIT(http://ocw.mit.edu/OcwWeb/Physics/8-251Spring-2005/CourseHome/index.htm).

Let us explain the fourth thesis in the context of a concrete example. QFTin its present state is in most cases not able to produce a convincing proofof a conjecture about a concrete Lagrangian model. But if this model is partof a larger class of models which can be characterized by certain structuralproperties, one is in a much better situation. An example is the Maldacenaconjecture about a possible connection between a special conformal theory (asupersymmetric gauge model) and a certain gravitational anti de Sitter (AdS)model. This conjecture has not been proven and according to our first remarkit is questionable that this will ever be possible. But since the generic rela-tion between AdS-QFT and a conformal theory on its boundary is an easilyestablished structural (model independent) fact (which is supported by AQFTin a exceptionally clear way), there is the interesting chance to come up witha mathematical theorem about which structural property on the conformal sideimplies/excludes a corresponding property on the AdS side. The rigorous resultof a structural investigation is that a standard conformal quantum field theorydescribed in terms of pointlike fields (e.g. a Lagrangian QFT) corresponds on

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the AdS side to a QFT which does not have sufficiently many degrees of freedomin order to be presentable in terms of Lagrangian pointlike fields. Vice versa, ifon starts with a standard theory on the AdS side there are too many degreesof freedom on the conformal side so that it is again not possible to relate thisstructure with any kind of Lagrangian QFT. Hence if the Maldacena conjecturewas meant to relate two standard Lagrangian field theories it is contradictedby a theorem. If on the other hand the conjecture involves a string theoryon the AdS side then nothing can be said because the structural propertiesof string theory which one would need for making structural comparisons arenot known. So instead of proving the conjecture one could perhaps turn theMaldecena conjecture into a working hypothesis and see whether the rigorousstructural properties which AQFT leads to on the AdS side are compatible withwhat one expects of a string theory; I am not aware of any such attempt. Butafter 30 years it is probably more realistic to believe that structural properties(of the kind one has been able to establish from the principles of QFT) maynever be available in string theory because it always may remain a collectionof prescriptions; after all there is no reason why any collection of not outrightcontradictory prescriptions can be backed up by a consistent theory. In otherwords the lack of structural understanding may not be the result of limitationson the part of string theorists, but rather may indicate that there is no coherenttheory in the standard sense of these words behind the string prescriptions.

Among the thousands of AdS-CFT papers I only know of three which ad-dress this problem, but the string community has ignored them. I think thatthis is not the result of a conscious act (a kind of intellectual boycott) but agenuine loss of understanding of what structural theorems are about. In thissituation it makes almost no difference whether this is plain ignorance or resultsfrom the kind of hubris about having a TOE at ones disposal; in short theseare the visible marks of a profound self-created crisis in particle physics. Withacclamation (instead of critical cutting edge arguments) it is much easier toenhance impact parameters for ones career. The present system of assigninghigh impact parameter to publication in certain journals which support fashin-able subject rewards acclamation and punishes attempts to look for antinomiesand breaking points (and thus doing research in the best of our traditions). Asmentioned before it is not difficult to find out about who is who in the admin-istration of the crisis in particle theory and verify that they enjoy a high socialstatus in the community of string theorists. No theory before string theory ledto such a deep schism in particle physics; not only have string theorist problemsto communicate with their more modest competitors from loop gravity, but alsothose part of QFT which are of a more conceptual nature and less suited forimmediate computational use for specific models (but very efficient to unravelstructures of families of models) are beyond string theoretic radar screens. Infact the unity of particle physics may already have been lost.

The last point in the list expresses concern with the future of particle physics.Given the human nature, it is very improbable that high-flying string theoristswho enjoyed social success and recognition in their globalized group and in themedia are able to muster the intellectual modesty which one needs in order to

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clean up ones desk and start something else; it is more realistic to expect thatthe present situation will continue or even aggravate.

In the past fundamental physics has proven remarkably resistent againstoutside pressure, neither the Nazis nor the Stalinists were able to make itsunderlying philosophy subservient to their ideologies. But its future state ofhealth depends crucially on whether the acting physicists are able to protect itagainst certain tendencies which already dominate our life through the economichegemomy of globalized capitalism, i.e. a kind of Enron-Worldcom-Parmetatanalog of physicists acquiring personal influence, wealth and fame at the expenseof the search for truth in physics.

Is science loosing its autonomy and are we reaching the end of the path whichbegun with Planck and Einstein? The recent book by Susskind [1] has broughtquestions like this into the forefront. In order to spare string theory the fate ofbecoming a kind of gigantic 20 century phlogiston (the obsolete pre-Lavoisiertheory of combustion) he proposes to change the meaning of what constitutesscience and to redefine of what makes an argument scientific.

Attempts to look for sociological causes behind paradigmatic changes inphysics are not new. After the discovery of quantum mechanics, P. Foreman[13] offered a sociological explanation for why these new ideas originated in war-shattered Germany. He made the argument that the unusual new indeterminismwhich originated from the probabilistic interpretation of quantum theory couldonly have been thought through in the necessary radical manner by individualswho saw their world destroyed. According to Foreman, those who were deeplyaffected by the gloom and doom Zeitgeist expressed in Spenglers influentialbook the demise of the west (which was widely red in post-war Germany) hadthe best precondition for being able to contemplate a new kind of mechanics inwhich acausality, indeterminism and chance played an important role.

This does not sound very palatable. Physics in war-shattered Germanyremained a strong autonomous science and QM has nothing to do with theSpengler kind of gloom; actually the influence went occasionally in the reversedirection e. i. misunderstandings of new developments in physics led to mis-leading philosophical and sociological interpretations16. If one wants to findmarks of the Zeitgeist in physics one should look less at the subject of researchand more to the manner in which physicist present their arguments and com-municate their findings; in the actual sociological setting a relevant questionwould be: do physicist uphold their traditional auto-critical manner or do theysuccumb to the forces of a neo-liberal globalized market economy where theexploration of the entertainment value by the media promises instant rewardand recognition. String theory serves as an excellent illustration of the powerwhich public relation has acquired in particle physics. Its negative influence isnot just the result of its highly speculative content and its lack of observability(which it shares with other previous fashions). More dangerous for the futureof particle physics are the attempts by its protagonists to elevate these flaws

16It is well-known that Einstein disliked the terminology relativity because his mainachievement was to identify the invariants which are independent of the observer.

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into a virtue and try to convince newcomers that there is no other game intown. That such attempts have a chance of success is very much related tothe conceptual confusions which already started at the cradle of this theory andbecame solidified as a result of its several revolutions during its more than 30years of existence. The conceptual dust it left on each of its crossroads of meta-morphoses prevented a return to the many interesting open problems which itleft behind; at no time before were so many computations done on such a muddyconceptual ground.

There is of course in addition the human element of what one may call apitbull syndrome17: after having invested almost 30 year of their scientificlife in making string theory work, its protagonists cannot let loose anymore.As a result we have to be prepared to coexist for a long time to come withstring theory, its supersymmetry support, its noncommutative spin-off and withwhatever big Latin letters stand for.

What might be the thoughts of a physicist 100 years from now who entersa physics library (assuming that nonelectronic publications will continue) andwalks along the corridors looking at those long shelves filled with hundred ofthousands of publications on supersymmetry, string theory and related subjects?Will he have similar thoughts as we have when we look at the great achievements100 years ago? Or will they be more similar to our thoughts when we look atpublications from the time of the pre-Lavoisier phlogiston theory of combustion(which was wrong despite the fact that it explained some observations)? If therewill be bad luck with the new generation of particle accelerators, and among ourdescendents there would be somebody with Paulis sarcasm, he might actuallypoint out that string theory was perfect: it predicted nothing and that wasexactly what was found.

Since hubris, prepotency and ignorance appear to be the hallmark of a hege-monic new Zeitgeist and physics does not seem to be left unaffected, it may beinteresting to know whether there exists a contemporary analog of Spenglerscritical socio-philosophical studies. A fundamental criticism of modernity is ex-tremely hard because of the problem to understand how in the midst of a highlycivilized culture with impressive contributions to music, arts, literature and sci-ence a monstrous crime of genocide can take place. This is precisely the startingpoint of Theodor Adornos critical analysis of modernity [14]. The part whichin my view is relevant for arts and sciences is his Dialectics of Enlightenment(with Max Horkheimer) his later essays on Kants criticism of pure reason aswell as on Negative Dialectics18. His focal point is the mechanism by whichrationality and enlightenment can turn into irrationality. Adorno illustrates hisideas mainly in arts and philosophy, but I think that an adaptation to scienceand in particular to the crisis in particle physics is possible and could shed more

17The pittbull is a combat dog which was bred in the UK during the second worldwar.Below a certain threshold of incitement it has the temper of a normal dog, beyond this it isincapable to let loose.

18These writings had an enormous impact on the postwar philosophy and sociology in Ger-many but (probably because they use all the resources of the German language and philosophy)they have not played a comperable role in the anglo-saxon cultural sphere.

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light on the points raised in the present essay.

2 Is it really the only game in town?

A guy with the gambling sickness loses his shirt every night in apoker game. Somebody tells him that the game is crooked, riggedto send him to the poorhouse. And he says, haggardly, I know, Iknow. But its the only game in town.Kurt Vonnegut, The Only Game in Town [15]This is a quotation from a short story by Kurt Vonnegut which Peter Woit

[16] recently used in one of the chapters in his forthcoming book entitled NotEven Wrong : The Failure of String Theory & the Continuing Challenge toUnify the Laws of Physics (using a famous phrase by which Wolfgang Paulicharacterized ideas which either had not even the quality of being wrong inan interesting way or simply lacked the scientific criterion of being falsifiable).The most prominent string theorist who used the no other game in townphrase in interviews when asked about alternatives by science journalists wasDavid Gross, and of course we do not know whether (despite his different socialconditions) he sometimes thinks along similar lines as the Vonnegut character.

In this section I would like to convince the reader why this statement iswrong; the sociological question why so many physicists seem to accept thisdictum was already addressed in the previous section. In order to avoid side-tracking the reader from my main aim which is just to answer the question intitle of this section (and not to use a criticism of string theory as a pretence forproselyting for approaches which have attracted my attention during the lastdecade) I will be scarce on references; the reader wants to have more informa-tion, it should not be too difficult to track down more relevant references.

My illustrations of alternative games are different from those by PeterWoit; in particular I have less faith in differential and algebraic geometry meth-ods in particle physics. As a result I also see the past Atiyah-Witten collabora-tion in a somewhat different light. On a superficial level, taking Wittens earlywork (e.g. on the screening effects of infrared clouds and the Kosterlitz-Thoulessphase transition) into account, I am inclined to see a negative influence morein the opposite direction from how Woit sees it. But on a more profound levelI find it very difficult to comment on a complex relation between two such em-inent scientist and prefer to leave the answer to historians of science, especiallysince it does not contribute anything to the theme at hand.

The way out which I advocate is to revisit some old unsolved deep concep-tual and mathematical problems which got lost in the dust on the wayside leftby several so-called revolutions. I believe that the deployment of new powerfulconceptual and mathematical tools of advanced QFT to such problems offer thebest hope for superseding the present crisis. This third way19 becomes particu-

19For the present discussion the first way denotes the speculative jump into a blue yonderand the a posteriori justification via conceptional and mathematical safeguarding; the secondway refers to cataclystic experimental discoveries.

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larly important if the first two ways failed (e.g. because a long-time speculativejourney into the blue yonder has led to a loss of conceptual orientation as it isthe case with string theory, or because the unreasonable efficiency of a high pa-rameter description with many conceptual deficiencies has led into a labyrinthi.e. the reality of the standard model) and the second path of experimentaldiscoveries gives no new clues (since high energy experiments are not any moreautonomous endeavors, but have an increasing dependence on the quality of theleading theory). This third way requires significant theoretical resources and iscertainly more difficult than that based on free-floating speculations. Its maintool are cutting edge arguments (including gedankenexperiments) by which ap-parent conceptual antinomies and gaps in a given setting are brought to thebreaking point so that the new structures can emerge in contrast to the existingones. The transition from the old quantum theory (with its strong experimentalbasis) to the new QM illustrates the power of this method. The first step isto become aware that quantum field theory, apart from the highly developedtechnology of perturbative renormalization, has remained an largely unfinishedbusiness; never mind its string theoretic caricature. Apart from some generalstructural consequences of the underlying principles (TCP, spin-statistics, theDHR theory of superselection sectors) I cannot think of any problem in QFTwhich was successfully solved and really brought to a closure in the sense asit happened a long time ago in other areas of fundamental physics e.g. QM.The post renormalization research in QFT has left us with an enormous amountof half-baked results even in those areas in which the theory was very success-ful on the observational side. A third way in QFT would primarily consist infinding an intrinsic formulation and computational methods which are not justprescriptions but follow directly from the underlying principles.

I have already touched upon some of these questions in the previous sectionwhen I referred to Jordans plea for a more intrinsic formulation of QFT withoutthe use of classical crutches and to the aborted S-matrix bootstrap approachas a potential start for an on-shell reformulation of QFT. Let us recall herealso the Wigner 1939 characterization of particles in terms of positive energyrepresentations of the Poincare group as the first completely intrinsic way to do(interaction-free) quantum physics without invoking any classical parallelism.Although it is of enormous conceptual value, it was certainly too limited forgenerating widespread attention since it said nothing about how to incorporateinteractions. There was however one conceptual spike in an otherwise perfectsetting. Whereas the relation of most finite energy representations with theLagrangian quantization approach for free fields was understood during thesubsequent two decades in terms of intertwiners between the Wigner canonicalrepresentations and their covariant counterparts, there were rather big positiveenergy families which resisted attempts to incorporate them into a setting ofLagrangian quantization. For the large infinite spin family20 there were manyfailed attempts by several generation of physicists to encode this representation

20For this family Wigners little group is the two-dimensional euclidean group whoseirreducible unitary representation lead to a continuous range of Casimir values correspondingto an infinite (half)integer helicity tower.

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into the setting of pointlike fields which finally found their explanation in aNo-Go theorem [17]. The remaining question of what is the best (sharpest)localization consistent with the infinite helicity tower led to the new concept ofstring-localization in the general setting of modular localization [18][19]. String-localized fields are operator-valued distributions A(x, e) which fluctuate in twospatial variables where x is a d-dimensional Minkowski spacetime point event atwhich the semiinfinite spacelike string starts and e is its the spacelike directional(unit) vector which (as far as far as covariance and fluctuations are concerned)can also be viewed as a point in a d-1 dimensional de Sitter space. For the(anti)commutator of two such fields to vanish it is not sufficient that the xsare spacelike, one string contour must also be outside the causal influence zoneof the other i.e. the string is visible in the sense of quantum localization[19](whereas that of a canonically quantized N-G string is fictitious apart from thelocalization of its centre of mass). This illustrates that it is not always thegrand design but little observations on the wayside which lead to interestingconceptual progress.

At this point it is helpful for the reader to be reminded that there are twoimportant concepts of localizations in relativistic quantum theory: the Newton-Wigner localization and modular localization. Whereas the N-W localizationresults from the adaptation of the Born x-space localization probability to rel-ativistic wave functions and connects to a position operator and associatedlocalization projectors and probabilities, modular localization results from theattempt to liberate the causal localization inherent in pointlike quantum fieldsfrom the non-intrinsic aspects of field-coordinatization. The lack of covarianceand causality of the N-W localization21 does not have any unpleasant conse-quences as long as one uses it in scattering theory; the fact that N-W local-ization regains covariance for asymptotically large separation makes it in factindispensable for the derivation of the Poincare-invariant S-matrix where theprojectors and their probability interpretation is crucial. The use of N-W lo-calization becomes however deadly wrong (superluminal acausalities) if usedfor propagation over finite distances. Modular localization [19] on the otherhand does not lead to projectors and probabilities but is the correct conceptfor the covariant causal localization of states and operator algebras. Unlikethe Lagrangian quantization, it is capable to control situation where a coor-dinatization by pointlike fields is impossible (as in the mentioned case of theWigner massless helicity tower representation). In such cases the issue of localfunctions, Wick polynomials, vacuum properties, an energy-momentum tensorand statistical mechanics properties are sufficiently different from the standardpointlike case and require new conceptual attention before deciding if such amatter is unnatural or has a role to play (e.g. in the astrophysical discussionof what constitutes black matter/energy22).

21More generally a theory with positivity of energy does not admit a system of covariantlocalization projectors.

22Despite the existence of KMS states on the infinite helicity tower string-localized fields,their thermal properties are quite unusual (as already nocticed by Wigner himself [18]) andremain essentially ununderstood.

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There are massiveWigner representations in d=1+2 dimensions with anoma-lous (non-halfinteger) spin whose associated fields have plektonic (braid group)statistics which is known to be inconsistent with a pointlike localization as wellwith an on-shell structure. More precisely even in the freest version (vanishingscattering cross section) the realization of braid group statistics requires thatany operator whose one-time application to the vacuum is a state with a one-particle component has necessarily a nonvanishing vacuum polarization cloud23

[23], in other words there is no on-shell free anyon field. Many properties ofanyons (anyon=abelian plekton) can be seen by applying modular localizationto the Wigner representation. Using similar modular intersection ideas as inthe case of factorizing models [24], there are good reasons to expect that in duetime one will have an explicit construction of integrable anyons.

It is somewhat surprising that modular localization within the Wigner set-ting also leads to new viewpoint about gauge theory. It was well known that thecovariant field description of the Wigner theory for massless helicity one rep-resentations relates to the electromagnetic field strength but does not supportthe introduction of pointlike vector potentials (without additional unphysicalextensions). This is very different from the classical situation where the posi-tivity of the quantum theoretical state space is of no relevance; in that case theidea of a gauge principle is useful in order to select among all possible covariantcouplings of a classical vector potential the Maxwells classical electrodynam-ics, This selection principle has a straightforward extension to the quasiclassicalrealm of quantum particles/fields in an external vector potential. The situationchanges radically if vector potentials become quantum objects. The standardway of handling this problem is to temporarily forget the positivity requirementand to uphold the pointlike structure so that the usual perturbative Lagrangianquantization approach could be applied. This is achieved by artificially extend-ing the quantum theory by adding in unphysical ghosts which at the end ofthe calculation have to be removed. From the outset it is not clear that afterhaving done the perturbation theory in this unphysical setting one can removethe ghosts from quantities which in classical sense would be gauge invariant andthe best formulation which makes such a descend manifest (by formulating thephysical descend as a cohomological problem) is the well known BRST formal-ism of gauge theory. There is nothing to say against doing this and gettinggood results for gauge invariant quantities. The problem starts if such a BRSTcatalyzer (Ghosts are neither in the original problem of spin one particlerepresentations nor in the final physical answers) is not considered as a tempo-rary computational trick, but becomes elevated to the status of a fundamentalphysical tool.

There are two arguments against accepting such a catalyzer.One is that in the quantum context one does not need a gauge principle

for the purpose of selecting between different possibility because (different from

23Only if one does not insist in the best localization which is stringlike but extends thelocalization space to a (Rindler) wedge one can even in the presence of interactions createpolarization-free states.

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interactions involving lower spin) unitarity and renormalizability24 already fixthe standard theory without the necessity of an additional choice. In differentwords the other non-gauge classical possibilities which are eliminated by thegauge principle do not occur in local quantum physics and hence there is noneed for a selecting gauge principle; to the contrary, accepting renormalizabilityas a principle of local quantum physics25, the classical gauge principle is thequasiclassical relic of a property of local quantum physics.

The second point is of a more philosophical nature in that the assignment of afundamental role to the BRST formalism would go against Heisenbergs dictumthat concepts (and if possible also computations) must be based on observables.In this context it is deeply satisfying that the Wigner theory, extended by theconcept of modular localization, leads to a physical string-localized potentialA(x, e) in the Fock space of photons [19]. The existence of this string-likeobject also explains an old observation in algebraic QFT stating that the oper-ator algebra generated by the field strength violates Haag duality for toroidalspacetime regions. All these statements have extensions to higher helicity rep-resentations and the case of helicity two, where the Wigner covariant fieldstrength is a 4-tensor with the algebraic properties of the Riemann tensor andwhere the string-localized potential is the metric 2-tensor of general relativity,is for obvious reasons particular interesting. Contrary to the field strength, theshort distance properties of the potentials do not grow with increasing helic-ity. But it is presently not known how to formulate interactions and set up aperturbation theory for string-like localized fields; as expected, the formal im-itation of the standard pointlike formalism leads to infrared divergencies. Soan alternative formulation of the content of gauge theory becomes synonymouswith the problem whether one is able to implement interactions starting withstring-localized physical vectorpotentials. It would be very interesting to makesome progress on this issue since the whole massless finite helicity family admitssuch physical string-localized ultraviolet-good-mannered potentials, even (as forhelicity=2) a BRST-like gauge formulation does not seem to be in sight [19].

Behind all these remarks is a theory, which after the Hilbert space oper-ator formulation of quantum mechanics is the most impressive examples of aperfect matching of physical and mathematical concepts: the modular (Tomita-Takesaki) theory of operator algebras and its unifying awe-abiding power torelate statistical mechanics, quantum field theoretical localization and the lo-cal quantum physical reason detre for the emergence of internal and externalsymmetries from general properties of operator algebras. Whereas the Hilbertspace theory was completely in place at the time of the discovery of QM and thephysicists only had to learn it26, the development of the modular theory in the

24In this argument there is an underlying tacit assumption that any quantum requirement(even if it is presently not completely understood) is more fundamental than a classical argu-ment i.e. quantum renormalizability explains the classical gauge principle in the quasiclassicallimit.

25This is reasonable because any quantum selection principle, even if presently insufficientlyunderstood, is more basic than a classical principle (even if completely understood)

26It is often overlooked that it was Fritz London [26] (and not John von Neumann) who

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middle 60s was a genuine give and take between physics and mathematics. In thephysical side it was Haag, Hugenholz and Winnink in their pursuit of statisticalmechanics for open systems (i.e. directly in the infinite thermodynamic infinitevolume limit, bypassing quantization boxes) where the true equilibrium ther-modynamics becomes valid without finite volume correction terms, who cameup with this new mathematical structure in a very spacial setting (physicistsusually do not aim at the generality of their arguments). One of their findingswas that in the thermal state the generator of the time translation has a two-sided symmetric spectrum and that this phenomenon is related to a symmetrybetween the observable algebra and its commutant. They also identified theso called KMS property as the characteristic thermal equilibrium property, thusgiving a fundamental significance to an observation which in the hands of Kubo,Martin and Schwinger was merely an analytic technical trick to avoid computingtraces for Gibbs states. On the mathematical side Tomita succeeded to pushthe modular property of group algebras (associated with the relation betweenright and left Haar measures) right into the heart of general operator algebras;Takesaki extended the theory and together with Winnink (shortly after the pro-tagonists from mathematicians and physics met at a conference 1967 in BatonRouge) made the relation with the physicists KMS structure whereas Connesused this new concepts (including the physicists terminology) to significantly ex-tend the classification of factor algebras started by Murray and von Neumann.It took another decade before the physicist Wichmann together with his youngPhD student and collaborator Bisognano discovered a geometrical aspect of thattheory in the setting of localized subalgebras of QFT; in this case they provedthat if the local algebras associated with spacetime regions are generated bypointlike fields, then the modular data of a wedge-localized algebra consists ofthe modular group being identical to the wedge-preserving Lorentz boost andthe Tomita involution being related to the reflection on the edge of the wedgewhich (up to a pi-rotation around the spatial axis perpendicular to the edge)is implemented by the famous TCP operator of QFT. The thermodynamicalKMS aspect attributed to the Lorentz boost (upon restriction of the vacuumstate to the wedge algebra) appeared at first sight a bit unusual. But afterSewell was able to connect this observation with another unexpected propertynamely Hawkings thermal radiation of black holes, and after Unruh analysedthe gedankenexperiment involving an uniformly accelerated observer in the fieldtheoretic vacuum, both situations became considerably de-mystified by findingtheir common root. The following years were characterized by a deepening ofstructural insight about operator algebraic modularity and its connections withgeometrical aspects of symmetry and localization (modular localization) as wellas thermal manifestation (localization thermality).

Within recent years the new framework of modular localization has entereda new phase. Whereas until recently it mainly served to study rather general

for the first time introduced this concepts of Hilbert space and rotations in Hilbert space(unitary operators) into quantum physics. Since at that time he was an assistant at the TUStuttgart, he was outside the quantum dialog and his paper went into oblivion despite anenthusiastic citation in Jordans paper on transformation theory [27].

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structural properties and prove mathematical theorems for families of QFTswhich shared certain properties, it became clear that it containes the longsought-after concepts for a new constructive approach. This approach for thefirst time in the history of QFT does not use the (quasi)-classical crutches ofLagrangian quantization. One of its first successful tests was to fill the abovementioned loopholes left by certain positive energy Wigner representation whoselocalization aspects cannot be described in terms of pointlike fields and whichescape Lagrangian quantization attempts.

Another successful application of modular localization led to a profound con-ceptual understanding of the bootstrap-formfactor construction for 2-dimensionalfactorizing models. Several years after the dreams of a unique S-matrix boot-strap came to an abrupt halt and its remainders became recycled into stringtheory of everything, some physicists made the modest observation that theS-matrix bootstrap can be made to work for special families of two-dimensionalintegrable models, the so-called factorizing models [25]. Far from being aTOE, the S-matrix bootstrap for factorizing S-matrices turned out to be thestart of something really interesting. The simpler structure of unitarity, cross-ing and covariance in the context of factorization permits not only to classifyfactorizing S-matrices, but also to start a formfactor formalism which leads toa unique determination of formfactors of would-be QFT models whose large-time asymptotic limits reproduce the bootstrap S-matrix. The implementationof crossing followed the field theoretic expectation (crossing as a collective effectof all intermediate states) and not the string theoretic duality (crossing solelyin terms of infinite one-particle towers).

Most of these results were obtained by adding additional recipes to the LSZframework of scattering theory which then led to unique multiparticle form-factors whose correctness was supported by consistency checks. These recipescomplicated however the recognition of the conceptual positioning of factoriz-ing models within the general setting of QFT, which is an important issue ifone wants to use them as a theoretical laboratory for a nonperturbative ac-cess to QFT and not just for their own sake. It turns out that these mod-els are characterized by the existence of vacuum-polarization-free generators(PFG) for wedge-localized algebras27 whose Fourier transforms are related toZamolodchikov-Faddeev algebras. Modular localization and interaction-causedvacuum polarization are inexorably related to causal locality i.e. to those prop-erties which are at the root of the sharp separation between QFT and anyform of relativistic QM. It is profoundly astonishing that the interaction-causedvacuum polarization, whose inexorable structural presence was first noted inthe standard setting of QFT way back by Furry and Oppenheimer (and whichhas been the cause of conceptional complexity in the particle-field relation), isnow returning as a central quantitative concept in the nonperturbative intrinsicconstruction of models.

Although in more realistic QFTs there are no PFGs which fulfill the phys-

27The wedge region is the smallest region for which the existence of PFGs is compatiblewith the presence of interactions.

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ically required operator domain properties [22], the idea that there may bea classification of (non-PFG, but nevertheless constructively accessible) gen-erators of wedge algebras even in the general case is very suggestive. Suchgenerators are non-local in the old sense, but their purpose is not the construc-tion of a nonlocal QFT28 but rather to use the structural simplicity gained byrelaxing localization29 in intermediate steps of the construction. Modular lo-calization theory assigns a preferred role to operator algebras associated withspatial wedge regions; in some sense which can be made precise wedge algebrasimplement the best compromise between particles and fields. As in the La-grangian quantization approach the perturbative construction of a model is inprinciple determined once one specified the Lagrangian, the QFT in the mod-ular localization setting is uniquely determined in terms of the structure of itswedge algebras (the position of the wedge algebra within the algebra of all oper-ators, or the algebraic structure of generators). The algebras for smaller regions(spacelike cones, double cones) are computed in terms of algebraic intersectionsof wedge algebras. Unlike the Lagrangian approach there is no place whereultraviolet divergences can occur; the worst which can happen is that the in-tersection of wedge algebras associated with double cone algebras is trivial (amultiple of the identity). In that case the expected local QFT associated withthe wedge data simply does not exist. In the Lagrangian approach there areno credible criteria for existence, but nobody really expects that Lagrangianmodels with nonrenormalizable short distance behavior can be associated withmathematically existing QFTs.

It is extremely interesting to note that modular localization unites threeimportant unsolved ideas from the past and places them into a new perspective.

The idea that a construction which avoids correlation functions in favor ofthe S-matrix and formfactors is necessarily free of ultraviolet divergencies;this is the extension of the old S-matrix bootstrap.

The idea of using instead of the rather singular quantum fields the localnet of spacetime-indexed operator algebras which they generate. This stepis analogous to the coordinate-independent setting achieved in moderndifferential geometry. It has been advocated by Haag since the end of the50s and as a result of a collective effort over several decades it grew intothe body of what is now called algebraic QFT or Local Quantum Physics[4].

The spirit underlying the Wigner representation theoretical approach tointeraction-free theories. This provides an illustration of intrinsicness (no

28The attempts to construct physically interpretable (macro-causal) nonlocal QFTs hasbeen marred by serious causality obstacles through all its history starting from the earlyMoeller-Kristensen work to the present attempts of noncommutative (and therefore necessarilynonlocal) theories [21].

29The Zamolodchikov-Faddeev algebra operators furnish the simplest illustration of suchwedge-algebra generators. The use of simple non-local operators for the construction of local-ized algebras is not limited to two dimensions [20].

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classical crutches) in a very special context, but in contrast to algebraicQFT, whose main use has been structural side, the Wigner classificationof positive energy representation and the associated algebraic net in Fockspace is totally constructive. One would like to be able to carry theseideas into the realm of interactions without being forced to introduce non-intrinsic field coordinatizations

In some way this could be considered as a renovation of some ideas of theold bootstrap S-matrix approach on a superior conceptual and mathematicallevel, but now not in antagonism to the off-shell localization concepts of QFTbut rather as a new conceptional enrichment. For two-dimensional models arigorous criterion for the solution of the age old problem of mathematical ex-istence (which perturbative Lagrangian quantization theory for known reasonscannot deliver) in form of a checkable degree of freedom property (analogousto modular nuclearity) for wedge algebras has been formulated and successfullytested for factorizing models [29]. Since the knowledge of wedge algebras (i.e.generating operators) is known to guaranty uniqueness of the possibly associ-ated local QFT, it is reasonable to expect that there exists an algebraic propertyrelated to the cardinality of degrees of freedom which also in the general casesecures the nontriviality of local intersections. As in the old days where theexistence of a theory was threatened by the bad short distance behavior in theintegration over fluctuations of singular pointlike field coordinates, in the newcompletely coordinatization- and singularity-free intrinsic setting the quantumphase space degree of properties decide whether a particular starting wedgealgebra structure leads to a QFT or not.

Perhaps it is helpful at this point to remind the reader that some of the greattheoretical discoveries of last century were made by re-thinking and re-workingalready existing theoretical elements. In Einsteins discovery of special relativ-ity, the formula for Lorentz transformation and its relation to Maxwells equationwas already noticed before but its revolutionary message for a new concept ofspacetime was not seen30. The great achievment of perturbative renormaliza-tion did not consist in discovering new principles underlying QFT, but ratherin implementing the known principles by new concepts and more appropriatecomputational technics which allowed to control certain aspects of ultravioletdivergences in terms of a more physical parametrization. Technically speakingthe old formulation of QFT which was heavily burdened by the quantum me-chanics formalism (Wenzel, Heitler) was traded with a manifestly relativistic onewhich placed the need to distinguish between Lagrangian (unrenormalized) pa-rameters and physical ones into a clearer perspective. Although both, QM andQFT are quantum theories, the inexorable presence of vacuum polarization andthe resulting significant structural changes make it impossible to picture QFTas some kind of relativistic quantum mechanics, a fact which even nowadays is

30There is a controversy among historians if Einstein who was on top of the ideas aroundthe turn of the 19 century may have known about these formulas perhaps unconciously. Inany case his derivation in his new spacetime interpretation is totally novel and extremelybeautiful.

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often overlooked [35].Although QFT is an amazingly successful framework when it comes to

agreement with experiments, the lack of any mathematically controllable model(apart from a special low-dimensional cases) and the absence of a comprehensiveconstructive strategy which explores the underlying principles without classi-cal crutches sets it apart from QM and most other area in theoretical physics.The crucial question, which arises from the aforementioned historical remarks,is whether a theory which has been around for more than 70 years and under-gone already one revolutionary change of its formalism allows yet another post-renormalization revolutionary step which would convert it into a autonomoustheory like previous theories. The existence of a radically different formu