Index
501
and SU(2) gauge invariance, 54–
60
Compton scattering in, 57
and renormalization group, 116–123
Quantization of non-Abelian gauge fields,
see Non-Abelian gauge fields,
quantization of
Quark flavour mixing
three generations, 320–324, 386, 407–
410
two generations, 306–308, 318–319
Quark masses, running, 134–135
Quasi-particle operators
in a superconductor, 221
in a superfluid, 205
Quenched approximation, 170
Regularization
and anomalies, 249–253
dimensional, 463–466
lattice, 151–152
Regular representation, see Representation, regular
Relevant coupling, 179, 181
Renormalizability
and large −q
2 behaviour in QED,
121–123
proof of, 84, 377
requirement, 84
of spontaneously broken gauge theories, 268
of theories with charged massive vector particles, 256–259
Renormalization
flow, 176–179
group, 73–74, 86, 116–123
and QCD corrections to parton
model, 135–148
group equation (RGE), 121, 130–
135
on the lattice, 172–182
in QED, 121–123
scale (μ), 118–121, 129, 142, 189
scheme, 127, 129, 188, 465
transformation, 176
and effective theory, 180
Representation
adjoint, 24, 44, 50, 111, 446
for antiparticles
in SU(2) f , 15–16
in SU(3) f , 20–21
basis for, 18
fundamental, 445
of SO(3), 445
of SU(2), 9, 445
of SU(3), 20, 445
of generators, in quantum field theory
for SU(2), 26–29
for SU(3), 30
irreducible, of SU(2), 14
matrix, of Lie algebras and groups,
14, 443–446
octet, in SU(3), 21–24, 83
regular, 24, 44, 50, 446
self, 446
singlet
in SU(2), 16–17
in SU(3), 22
triplet
in SU(2), 17–18
in SU(3), 20
Resolution parameters, 105
R gauges, 274
ρ parameter, 386, 414–416, 433
Rooting, 170, 187
Running coupling constant, 103–104, 115,
123–129
Running mass, 134–135
Rutherford process, 92–93
Scaling, 135
violations, 140, 314
in deep inelastic scattering, 134–
148
in e
+ e
− → hadrons, 114–115
Scattering, hard, and QCD tree graphs,
86–97
Screening current, 262–263, 268
Screening, in Higgs sector, 418–419
Screening length, 262–263
Schr¨ odinger picture, 162
Sea quarks, 89–90
See-saw mechanism, 407
Semi-leptonic processes, 305
σ-model
linear, 239–242
non-linear, 243–245
501
and SU(2) gauge invariance, 54–
60
Compton scattering in, 57
and renormalization group, 116–123
Quantization of non-Abelian gauge fields,
see Non-Abelian gauge fields,
quantization of
Quark flavour mixing
three generations, 320–324, 386, 407–
410
two generations, 306–308, 318–319
Quark masses, running, 134–135
Quasi-particle operators
in a superconductor, 221
in a superfluid, 205
Quenched approximation, 170
Regularization
and anomalies, 249–253
dimensional, 463–466
lattice, 151–152
Regular representation, see Representation, regular
Relevant coupling, 179, 181
Renormalizability
and large −q
2 behaviour in QED,
121–123
proof of, 84, 377
requirement, 84
of spontaneously broken gauge theories, 268
of theories with charged massive vector particles, 256–259
Renormalization
flow, 176–179
group, 73–74, 86, 116–123
and QCD corrections to parton
model, 135–148
group equation (RGE), 121, 130–
135
on the lattice, 172–182
in QED, 121–123
scale (μ), 118–121, 129, 142, 189
scheme, 127, 129, 188, 465
transformation, 176
and effective theory, 180
Representation
adjoint, 24, 44, 50, 111, 446
for antiparticles
in SU(2) f , 15–16
in SU(3) f , 20–21
basis for, 18
fundamental, 445
of SO(3), 445
of SU(2), 9, 445
of SU(3), 20, 445
of generators, in quantum field theory
for SU(2), 26–29
for SU(3), 30
irreducible, of SU(2), 14
matrix, of Lie algebras and groups,
14, 443–446
octet, in SU(3), 21–24, 83
regular, 24, 44, 50, 446
self, 446
singlet
in SU(2), 16–17
in SU(3), 22
triplet
in SU(2), 17–18
in SU(3), 20
Resolution parameters, 105
R gauges, 274
ρ parameter, 386, 414–416, 433
Rooting, 170, 187
Running coupling constant, 103–104, 115,
123–129
Running mass, 134–135
Rutherford process, 92–93
Scaling, 135
violations, 140, 314
in deep inelastic scattering, 134–
148
in e
+ e
− → hadrons, 114–115
Scattering, hard, and QCD tree graphs,
86–97
Screening current, 262–263, 268
Screening, in Higgs sector, 418–419
Screening length, 262–263
Schr¨ odinger picture, 162
Sea quarks, 89–90
See-saw mechanism, 407
Semi-leptonic processes, 305
σ-model
linear, 239–242
non-linear, 243–245