502
Index
Soft divergences, 101–102, 104
Soft pion process, 231
Spin waves, 201–202
Splitting function, 141, 144
Spontaneously broken symmetry, see Symmetry, spontaneously broken
Subsidiary condition, 61
Superconductor, BCS, 219–225, 260–261
generation of photon mass in, 260–
263
type I, 268
type II, 268
Superfluid, Bogoliubov, see Bogoliubov,
superfluid
Supersymmetry, 422
Symanzik improved action, 182, 187, 190
Symmetry
chiral, 31–37, 53
breaking, 37, 227–248
in lattice field theory, 156–158
current, see Current, symmetry
hadronic isospin, 12–18
non-Abelian global, 3–38
in quantum field theory, 24–38
non-Abelian local, 39–70
in quantum field theory, 51–70
SO(3), 438–439, 450–452
irreducible representations of, 14
Lie algebra of, 439
relation with SU(2), 450–452
structure constants of, 439
triplet, 17–18
SO(4), 240, 440–441
spontaneously broken, 37, 195–279
chiral, 3–4, 227–253
in condensed matter physics, 198–
209
global, 195–226
global Abelian, 211–216
global non-Abelian, 216–219
local, 255–279
local Abelian, 264–274
local non-Abelian, 275–279
mass generation via, 5, 228–230,
255, 260–264, 275–279
and non-zero vev, 209–210
SU(2), 8, 439–440
chiral, 35–36
custodial, 415–418
flavour, 3, 5–18, 231
generators of, 9, 440
global, 3
infinitesimal transformation, 8
Lie algebra of, 14, 440
local, 4, 40–49, 51–53
matrix, general form of, 7–10
relation with SO(3), 450–452
singlet, 16–17
structure constants of, 14
triplet, 17–18
SU(2) f5 , 231
SU(3), 18, 442–443
chiral, 36
colour, 4, 78–84
flavour, 3, 18–24
generators of, 19, 442
global, 3, 18–24
Lie algebra of, 19, 442
local, 4, 49–53
matrix, general form of, 19
octet, 21–24, 50–51
singlet, 22
structure constants of, 19, 443
SU(3) f5 , 232
SU(2) fL × SU(2) fR , 231–235, 240–
245
SU(2) × U(1), 217–219
SU(2)L × U(1), 380
SU(3) fL × SU(3) fR , 247–248
weak isospin, 41
Technicolour models, 279, 422
Tensor
covariant derivative as, 456
field strength
SU(2), 48–49
SU(3), 51
U(1), 48
hadron, 99–100
weak, 309
lepton, 99–100
in V-A theory, 299–300, 309
Riemann curvature, 461
θ-term, 84–86
θW, see Mixing angle, weak (θW)
Thomson atom, 88
’t Hooft’s gauges, 271–274, 278, 377
Index
Soft divergences, 101–102, 104
Soft pion process, 231
Spin waves, 201–202
Splitting function, 141, 144
Spontaneously broken symmetry, see Symmetry, spontaneously broken
Subsidiary condition, 61
Superconductor, BCS, 219–225, 260–261
generation of photon mass in, 260–
263
type I, 268
type II, 268
Superfluid, Bogoliubov, see Bogoliubov,
superfluid
Supersymmetry, 422
Symanzik improved action, 182, 187, 190
Symmetry
chiral, 31–37, 53
breaking, 37, 227–248
in lattice field theory, 156–158
current, see Current, symmetry
hadronic isospin, 12–18
non-Abelian global, 3–38
in quantum field theory, 24–38
non-Abelian local, 39–70
in quantum field theory, 51–70
SO(3), 438–439, 450–452
irreducible representations of, 14
Lie algebra of, 439
relation with SU(2), 450–452
structure constants of, 439
triplet, 17–18
SO(4), 240, 440–441
spontaneously broken, 37, 195–279
chiral, 3–4, 227–253
in condensed matter physics, 198–
209
global, 195–226
global Abelian, 211–216
global non-Abelian, 216–219
local, 255–279
local Abelian, 264–274
local non-Abelian, 275–279
mass generation via, 5, 228–230,
255, 260–264, 275–279
and non-zero vev, 209–210
SU(2), 8, 439–440
chiral, 35–36
custodial, 415–418
flavour, 3, 5–18, 231
generators of, 9, 440
global, 3
infinitesimal transformation, 8
Lie algebra of, 14, 440
local, 4, 40–49, 51–53
matrix, general form of, 7–10
relation with SO(3), 450–452
singlet, 16–17
structure constants of, 14
triplet, 17–18
SU(2) f5 , 231
SU(3), 18, 442–443
chiral, 36
colour, 4, 78–84
flavour, 3, 18–24
generators of, 19, 442
global, 3, 18–24
Lie algebra of, 19, 442
local, 4, 49–53
matrix, general form of, 19
octet, 21–24, 50–51
singlet, 22
structure constants of, 19, 443
SU(3) f5 , 232
SU(2) fL × SU(2) fR , 231–235, 240–
245
SU(2) × U(1), 217–219
SU(2)L × U(1), 380
SU(3) fL × SU(3) fR , 247–248
weak isospin, 41
Technicolour models, 279, 422
Tensor
covariant derivative as, 456
field strength
SU(2), 48–49
SU(3), 51
U(1), 48
hadron, 99–100
weak, 309
lepton, 99–100
in V-A theory, 299–300, 309
Riemann curvature, 461
θ-term, 84–86
θW, see Mixing angle, weak (θW)
Thomson atom, 88
’t Hooft’s gauges, 271–274, 278, 377