496
Index
Fermion (contintued)
overlap, 158, 247
propagator, in lattice field theory,
155–157
staggered, 157, 170, 187
Wilson, 155–157, 190
Ferromagnet, 199–202, 213–214
Feynman
rules for tree graphs
in electroweak theory, 474–479
in QCD, 473–474
sum over paths formulation of quantum theory, 162–170
fermions in, 169–170, 467–471
gauge-fixing in, 69
propagators in, 167
Field strength tensor, see Tensor, field
strength
Fine-tuning, of Higgs mass, 182, 422
Finite-size effects, 182
Fixed point (in RGE), 133, 176–177
infrared stable, 133, 178
infrared unstable, 178
of renormalization transformation,
176
ultraviolet stable, 133
and zero of β function, 133
Flavours, number of active, 309, 315
Flavour tagging, 335–338, 347
Flux quantization, in a superconductor,
267–270
Four-fermion interaction, 286
effective (non-leptonic), 324
not renormalizable, 297, 369, 374
and violation of unitarity, 368–369
Fundamental representation, see Representation, fundamental
gA, 238
γ5 matrix, 32
Gamma function, 464
Gap equation, in BCS theory, 224
Gauge
connection, 458
field, geometrical aspects of, 453–
462
fixing
for SU(2), 52, 61–62
’t Hooft’s, 273–274, 278
for U(1), 60–61
principle, 3, 46, 83
R, 274
theory
electromagnetism as, 458
reason for, in weak interactions,
255, 373, 377
SU(2), 40–49, 51–53
SU(3), 49–51, 53
transformation
Abelian, 3, 41, 57, 158, 255, 261,
265–267
geometrical analogy for, 454
non-Abelian, 3, 42–45, 49–53, 57,
276
U, 274, 276
Gell-Mann matrices, 19, 442–443
Gell-Mann–Nishijima relation, 20, 380
Gell-Mann–Okubo formula, 248
Generations
and anomaly cancellation, 253
three, mixing in, 317–324, 407–410
two, mixing in, 306–308, 318–319
Generators, 437–438
Lorentz group, 441–442
SO(3), 438–439
SO(4), 440–441
SU(2), 9, 439–440
in quantum field theory, 26
SU(3), 19, 442–443
in quantum field theory, 30
SU(2) × SU(2), 441
in quantum field theory, 232–233
U(1), in quantum field theory, 25
GF, 294, 297, 305–306, 362, 368–370, 374,
383–384, 412
Ghosts, 69–70
GIM (Glashow–Iliopoulos–Maiani) argument, 306–308
and charm hypothesis, 306
mixing, 306–308
weak neutral current, 307
diagonal in flavour, 307–308
Ginsparg–Wilson relation, 157
Ginzburg–Landau theory, 260–263, 278
Gluon fusion, 425–426
Index
Fermion (contintued)
overlap, 158, 247
propagator, in lattice field theory,
155–157
staggered, 157, 170, 187
Wilson, 155–157, 190
Ferromagnet, 199–202, 213–214
Feynman
rules for tree graphs
in electroweak theory, 474–479
in QCD, 473–474
sum over paths formulation of quantum theory, 162–170
fermions in, 169–170, 467–471
gauge-fixing in, 69
propagators in, 167
Field strength tensor, see Tensor, field
strength
Fine-tuning, of Higgs mass, 182, 422
Finite-size effects, 182
Fixed point (in RGE), 133, 176–177
infrared stable, 133, 178
infrared unstable, 178
of renormalization transformation,
176
ultraviolet stable, 133
and zero of β function, 133
Flavours, number of active, 309, 315
Flavour tagging, 335–338, 347
Flux quantization, in a superconductor,
267–270
Four-fermion interaction, 286
effective (non-leptonic), 324
not renormalizable, 297, 369, 374
and violation of unitarity, 368–369
Fundamental representation, see Representation, fundamental
gA, 238
γ5 matrix, 32
Gamma function, 464
Gap equation, in BCS theory, 224
Gauge
connection, 458
field, geometrical aspects of, 453–
462
fixing
for SU(2), 52, 61–62
’t Hooft’s, 273–274, 278
for U(1), 60–61
principle, 3, 46, 83
R, 274
theory
electromagnetism as, 458
reason for, in weak interactions,
255, 373, 377
SU(2), 40–49, 51–53
SU(3), 49–51, 53
transformation
Abelian, 3, 41, 57, 158, 255, 261,
265–267
geometrical analogy for, 454
non-Abelian, 3, 42–45, 49–53, 57,
276
U, 274, 276
Gell-Mann matrices, 19, 442–443
Gell-Mann–Nishijima relation, 20, 380
Gell-Mann–Okubo formula, 248
Generations
and anomaly cancellation, 253
three, mixing in, 317–324, 407–410
two, mixing in, 306–308, 318–319
Generators, 437–438
Lorentz group, 441–442
SO(3), 438–439
SO(4), 440–441
SU(2), 9, 439–440
in quantum field theory, 26
SU(3), 19, 442–443
in quantum field theory, 30
SU(2) × SU(2), 441
in quantum field theory, 232–233
U(1), in quantum field theory, 25
GF, 294, 297, 305–306, 362, 368–370, 374,
383–384, 412
Ghosts, 69–70
GIM (Glashow–Iliopoulos–Maiani) argument, 306–308
and charm hypothesis, 306
mixing, 306–308
weak neutral current, 307
diagonal in flavour, 307–308
Ginsparg–Wilson relation, 157
Ginzburg–Landau theory, 260–263, 278
Gluon fusion, 425–426