Relativistic Quantum Mechanics - Bjorken and Drell

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A basic book describing the relativistic Quantum Mechanics by Bjorken and Drell

Text of Relativistic Quantum Mechanics - Bjorken and Drell

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  • INTERNATIONAL SERIES IN PURE AND APPLIED PHYSICSLeonard I. Schifr, Consulting Editor

    Allis and, Herlin Thermodynamics and St'atistical MechanicsBecker Introduction to'l'heoretical MechanicsBjorken and DreII Relativistic Quantum MechanicsClark Applied X-raYsColtin Field Theory of Guided WavesEaans The Atomic NucleusFinkelnburg Atomic PhYsicsGinztoi Microwave MeasurementsGreen Nuclear PhYsicsCurney Introduction to Statistical MechanicsHatl Introduction to Electron MicroscopyHard,y ancl Percin The Principles of OpticsHarnwell Electricity and ElectromagnetismHarnwell and Liaingood Experimental Atomic PhysicsIlarnwell and' Stephens Atomic PhysicsHenley and Thirring Elementary Quantum tr'ield TheoryHouston Principles of Mathematical PhysicsHund High-frequency MeasurementsKennard, Kinetic TheorY of GasesLane Superfluid PhYsicsLeighton Principles of Modern PhysicsLind,say Mechanical Radiation iLioingston and Blewett Particle AccelerbtorsMiddieton An Introduction to Statistical Communication TheoryMorse Vibration and Sound

  • Morse and Feshbach Methods of Theoretical PhysicsMuskat Physical Principles of Oil ProductionPresent Kinetic Theory of GasesRead Dislocations in CrystalsRichtrnyer, Kennard, and. Lauritsen Introduction to Modern phvsicsSchiff QuantumMechanicsSeitz The Modern Theory of SolidsSlater fntroduction to Chemical PhysicsSlater Quantum Theory of Atomic Structure, Vol. ISlater Quantum Theory ofAtomic SJructure, Vol. IISlater Quantum Theory of MatterSlater Quantum Theory of Molecules and Solids, Vol. ISlater Quantum Theory of Molecules and Solids, Vol. 2Sla,ter and Frank ElectromagnetismSlater and, Franh Introduction to Theoretical phvsicsSlater and Frank MechanicsSmythe 'Static and Dynamic ElectricityStrdtton r.Electromagnetic TheoryTinkharn Group Theory and Quantum MechanicsTounes and, Scha.u:Iow Microwave Spectroscop]rWhite Introduction to Atomic Spectra

    The late F. K. Richtmler lvas consulting Editor of the series lrom its inception in1929 to his death in 1939. Lee A. DuBridge was consulting Editor from r9J9tro l!46; aud G. P. Harnwell from 194? to I9S4.

  • James D. Bjorken Sidney D. DrellAssociate ProJessor

    S tanJ ord. Linear Accelerqtor CenterStanJord' Unioersity

    McGraw-Hill Book Cornpa,nyNero York St. Louis Scln Francisco Toronto Lond'on S5rd'ney

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    copyright @ 1964 by McGraw-Hill, Inc. All Rights Reserved. printed inthe United States of America. This book, or parts thereof, may not bereproduced in any form without permission of the publishers.

    Library of Congress Catalog Card Number 6B-ZLZZ}7 8 9 1 0 1 1 1 2 - M A M M - 7 5 4 3 2 L O05493 \

  • PrefaceThe propagutor,'approach to a relativis\ic quant'um theory. pioneeredin rg+g by Feynman has provided a practical, as well as intuitivelyappealing, formulation of quantum electrodynamics and a fertileapproaclt to a broad class of problems in the theory of elementaryputti"t".. The entire renormalization program, basic to the presentconfidence of theorists in the predictions of quantum electrodynamics,is in fact dependent on a Fe5rnman graph analysis, as is also con-siderable progr"u. in the proofs of analytic properties required,to writedispersion relations. Indeed, one may go so far as to adopt theextreme view that the set of all Feynman graphs is the theory'

    we do not advocate this view in this book nor in its companion

  • Yllt Prcfaee

    volume, "Relativistic Quantum !'ields," nor indeed do we advocateany single view to the exclusion of others. The unsatisfactory statusof present-day elementary particle theory does not allow one such aluxury. In particular, we do not, wish to minimize the importance ofthe progress achieved in formal quantum field theory nor the con-siderable understanding of low-energy meson-nucleon processes givenby dispersion theory. However, we give first emphasis to the develop-ment of the Feynman rules, proceeding directly from a particle waveequation for the Dirac electron, integrated with hole-theory boundaryconditions.

    Three main convictions guiding us in this approach were theprimary motivation for undertaking this book (later to become books):

    1. The Feynman graphs and rules of calculation summarizequantum field theory in a form in close contact with the experimentalnumbers one wants to understand. Although the statement of thetheory in terms of graphs may imply perturbation theory, use ofgraphical methods in the many-body problem shows that this formal-ism is flexible enough to deal with phenomena of nonperturbativecharacter (for example, superconductivity and the hard-sphere Bosegas) .

    2. Some modification of the Feynnian rules of calculation maywell outlive the elaborate mathematical structure of local canonicalquantum field theory, based as it is on such idealizations as fieldsdefined at points in space-time. Therefore, let us develop these rulesfirst, independently of the field theory formalism which in time maycome to be viewed more as a superstructure than as a foundation.' 3. Such a development, more direct and less formal-if less com-pelling-than a deductive field theoretic approach, should bringquantitative calculation, analysis, and understanding of Feynmangraphs into the bag of tricks of a much larger cornmunity of physiciststhan the specialized narrow bne of second quantized theorists. Inparticular, we have in mind our experimental colleagues and studentsinterested in particle physics. We believe this would be a healthydevelopment.

    Our original idea of one book has grown in time to two volumes.In the first book, "Relativistic Quantum Mechanics," we develop apropagator theory of Dirac particles, photons, and Klein-Gordonrnesons and perform a series of calculations designed to illustratevarious useful techniques and concepts in electrornagnetic, weak, andstrong interactions. These include defining and implementing therenormalization program and evaluating effects of radiative correc-

  • Preface lx

    tions, such as the Lamb shift, in low-order calculations. The recessarybackground for this book is provided by a course in nonrelativisticquantum mechanics at the general level of schifl's text ,,euantumMechanics."

    In the second book, ,,Relativistic euantum Fields,,, we developcanonical field theory, and after constructing closed expressions forpropagators and for scattering amplitudes with the LSZ reducliontechnique, return to the Feynman graph expansion. The perturbationexpansion of the scattering amplitude constructed by canonical fieldtheory is shown to be identical with the Feynman rules in the firstbook. with further graph analysis we study anaryticity properties ofFeynman amplitudes to arbitrary orders in the coupling parameterand illustrate dispersion relation methods. Finally, we prove thefiniteness of renormalized quantum electrodynamics to each order ofthe interaction.

    Without dwelling further on what we do, we may list the majortopics we omit from discussion in these books. The development ofaction principles and a formulation of quantum field theory from avariational approach, spearheaded largely by schwinger, are on thewhole ignored. we refer to action variations only in search of sym-metries. There is no detailed discussion of the powerful developmentsin axiomatic field theory on the one hand and the purely g-matrixapproach, divorced from field theory, on the other. Aside from adiscussion of the Lamb shift and the hydrogen atom spectrum in thefirst book, the bound-state problem is ignored. Dynamical applica-tions of the dispersion relations are explored only minimaliy. Aformulation of a quantum field theory for massive vector mesonsls notgiven-nor is a formulation of any quantum field theory with deriva-tive couplings. Finally, we have not prepared a bibliography of allthe significant original papers underlying many of the developmentsrecorded in these books. Among the following recent excelleni booksor monographs is to be found the remedy for one or more of thesedeficiencies:

    Schweber, S.: "An Introduction to Relativistic euantum Field Theory,r' NewYork, Harper & Row, Publishers, Inc., 1961.

    Jauch, J. M., and F. Rohrlich: "The Theory of photons and Electrons." cam-bridge, Mass., Addison-Wesley Publishing Company, Inc., 1g5b.

    Bogoliubov, N. N., and D. v. shirkov: "Introduction to the Theory of euantizedFields," New York, fnterscience publishers, Inc., Lg5g.Akhiezer, A., and V. B. Bereztetski: .,euantum Electrodynamics,', 2d ed., New

    York, John Wiley & Sons, Inc., 1g68.umezawa, H.: "Quantum Field rheory," Amsterdam, North Hoiland pub\shing

    Company, 1956.

  • PreJace

    Eamilton, J.: "Theory of Elementary Particles," London, Oxford UniversityPress, 1959.

    Mandl, F.: "Introduction to Quantum Field Theory," New York, IntersciencePublishers, Inc., 1960.

    Roman, P.: "Theory of Elementary Particles," Amsterdam, North HollandPublishing Company, 1960.

    Wentzel, G.: "Quantum Theory of Field," New York, Interscience Publishers,Inc., 1949.

    Schwinger, S.: "Quantum Electrodynamics," New York, Dover Publications,Inc., 1958.

    Feynman, R. P.: "Quantum Electrodynamics," New York, W. A. Benjamin,Inc., 1962.

    Klein, L. (ed.): "Dispersion Relations and the Abstract Approach to Field Theory,"New York, Gordon and Breach, Science Publishers, Inc., 1961.

    Screaton, G. R. (ed.): "Dispersion Relations; Scottish Universities SummerSchool," New York, Interscience Publishers, Inc., 1961.

    Chew, G. F.: "S-Matrix Theory of Strong Interactions," New York, W. A'Benjamin, Inc., 1962.fn conclusion, we owe thanks to the many students and colleagues

    who have been invaluable critics and soundin