284
Index
E
Effective dynamics, 229
Elitzur theorem, 257
Energy bounded below, 22
Energy–momentum renormalized density,
32
F
Fermi gas, 160
First order formalism, 18
Fock representation, 70
Folium, 79
F W exponential field algebra, 269
F W local exponential algebra, 270
G
Galilei group, 240
breaking, 240
Galilei symmetry breaking, 172
Gauge fixing, 252
Gauge Principle, 251
Gauge symmetry breaking, 115
Gauss constraint, 268
Gauss constraint and non-regular representation, 269
Gauss invariant vacuum, 269, 270
Gauss operators, 269
Gauss subgroup, 269
Gibbs states, 148
Global gauge symmetry, 249
broken, 250
operational meaning, 250
GNS
representation, 76
theorem, 76
Goldstone bosons, 169
Goldstone excitations, 235
Goldstone spectrum, 235
Goldstone spectrum with energy gap, 247
Goldstone theorem, 169
classical fields, 47
local relativistic fields, 182
mathematical discussion, 172
non-symmetric Hamiltonians, 199
non-zero temperature, 168
Ground state
non symmetric, 8
uniqueness, 76, 102
H
Heisenberg algebra, 73
Higgs mechanism, 172, 257
non perturbative, Coulomb gauge, 195
non-perturbative, local gauges, 205
perturbative approach, 203
Higgs mechanism and EDDG theorem, 205
Hilbert Space Sector (HSS), 23
Homotopy classes, 271
I
Infrared renormalization, 232, 233
Initial data, locally regular, 18
Instanton winding number, 266, 273
Ising model
Bogoliubov strategy, 136
cyclic boundary conditions, 143
free boundary conditions, 140
Goldstone strategy, 134
periodic boundary conditions, 136
Ruelle strategy, 135
symmetry breaking boundary conditions, 143
J
Jellium model, 237
infrared regular states, 238
variables at infinity, 238
K
Kink, 42
KMS condition, 148
KMS state
extremal, 156
primary, 156
Kogut-Susskind dipole ghosts, 267
L
Landau phonons, 169
Large gauge transformations, 271
Lipschitz condition, local, 19
Local algebra, 96
Local gauge group, 251
Local gauge group topology, 270
Local gauge invariance
non deterministic time evolution, 251
Local gauge symmetry, 249, 251
Local Gauss Law, 253
Local Gauss law, 259
Local Gauss law on physical states, 254
Local generation of symmetries and boundary terms, 234
Locality, 96
Index
E
Effective dynamics, 229
Elitzur theorem, 257
Energy bounded below, 22
Energy–momentum renormalized density,
32
F
Fermi gas, 160
First order formalism, 18
Fock representation, 70
Folium, 79
F W exponential field algebra, 269
F W local exponential algebra, 270
G
Galilei group, 240
breaking, 240
Galilei symmetry breaking, 172
Gauge fixing, 252
Gauge Principle, 251
Gauge symmetry breaking, 115
Gauss constraint, 268
Gauss constraint and non-regular representation, 269
Gauss invariant vacuum, 269, 270
Gauss operators, 269
Gauss subgroup, 269
Gibbs states, 148
Global gauge symmetry, 249
broken, 250
operational meaning, 250
GNS
representation, 76
theorem, 76
Goldstone bosons, 169
Goldstone excitations, 235
Goldstone spectrum, 235
Goldstone spectrum with energy gap, 247
Goldstone theorem, 169
classical fields, 47
local relativistic fields, 182
mathematical discussion, 172
non-symmetric Hamiltonians, 199
non-zero temperature, 168
Ground state
non symmetric, 8
uniqueness, 76, 102
H
Heisenberg algebra, 73
Higgs mechanism, 172, 257
non perturbative, Coulomb gauge, 195
non-perturbative, local gauges, 205
perturbative approach, 203
Higgs mechanism and EDDG theorem, 205
Hilbert Space Sector (HSS), 23
Homotopy classes, 271
I
Infrared renormalization, 232, 233
Initial data, locally regular, 18
Instanton winding number, 266, 273
Ising model
Bogoliubov strategy, 136
cyclic boundary conditions, 143
free boundary conditions, 140
Goldstone strategy, 134
periodic boundary conditions, 136
Ruelle strategy, 135
symmetry breaking boundary conditions, 143
J
Jellium model, 237
infrared regular states, 238
variables at infinity, 238
K
Kink, 42
KMS condition, 148
KMS state
extremal, 156
primary, 156
Kogut-Susskind dipole ghosts, 267
L
Landau phonons, 169
Large gauge transformations, 271
Lipschitz condition, local, 19
Local algebra, 96
Local gauge group, 251
Local gauge group topology, 270
Local gauge invariance
non deterministic time evolution, 251
Local gauge symmetry, 249, 251
Local Gauss Law, 253
Local Gauss law, 259
Local Gauss law on physical states, 254
Local generation of symmetries and boundary terms, 234
Locality, 96