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All problems with renormalizing infinities can
be resolved by considering
of our theory(ies)of our theory(ies)
The Small Distance Limit
Scaling and Dimensions4Examples: theory
410 210 1 210
distance scale
2, e
2and: Electro-magnetism, e
Compare large distance with small distance:
At large distance scales, thecurvature is weak near linearity = weak interactions
At small distances, strongcurvature strong interactions
The quantum fluctuations at small distancein such a theory undermine its own structure.
Its small-distance behaviour is ILL-DEFINED
Spontaneous symmetry breaking( left - right symmetry )
At short distancescales, our particle
theory lookslike this
At large distancescales, the situationis as described here
This degree offreedom corresponds to
the Higgs particle
Breaking Rotational Symmetry
Now THIS becomes an essential degree
of freedomAnd THIS is theHiggs degree of
Freedom
If there were no HIGGS particle in ourtheory, then the “Mexican Hat” would
be infinitely steep, or:
HiggsM This is exactly like the situation in a
“chiral field theory”:2 2F
Such a theory is ill-defined, since itssmall-distance structure runs out of control...
Leptons
Quarks
Generation I Generation II Generation IIIThe Standard Model
Gauge Bosons g
us s
e
u
c
c
b b
b b
t t
0Z
dt
c
s
e
u
c t
b
s
W
du t
W
e
u
c t
d
Graviton
L L L
e
u
d
c
s
d
s b
d
Higgs
L L L
R R R
RRR
Running Coupling Strengths
*
**
***
*
**
***
strongg
Elect-MagneWeakg
*
*
*
310 610 910 1210 1510 18101 GeV
1
0.5
Super symmetric theories
strongg
Elect-MagneWeakg
*
*
*
*
**
*
**
*
**
***
310 610 910 1210 1510 18101 GeV
1
0.5
Otherwise, it is likely toexplode ….
A theory can only be successfulif we understand completelyhow its dynamical variables
behave at the tiniest possibletime- and distance scales