Zakrzewski W.J. — Low Dimensional Sigma Models :: Электронная библиотека попечительского совета мехмата МГУ

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Zakrzewski W.J. — Low Dimensional Sigma Models

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Название: Low Dimensional Sigma Models

Автор: Zakrzewski W.J.

Аннотация:

This book gathers together established ideas and applications of sigma models and presents them together with modern applications to provide a unified and complete view of simple sigma models and the role they play in model building in field theoretical methods in elementary particle physics. The book is written for both mathematicians and physicists and is aimed at graduate students and researchers in theoretical particle physics who are interested in sigma models and those working in the general area of harmonic maps in pure mathematics.

Язык:

Рубрика: Физика/

Серия: Сделано в холле

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1989

Количество страниц: 301

Добавлена в каталог: 04.10.2012

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$\lambda\phi^{4}$ theory      111
$\mathbb{C}P^{1}$ skyrmions      224
$\mathbb{C}P^{N-1}$ electrodynamics      126
$\mathbb{C}P^{N-1}$ model      49 51
$\mathbb{C}P^{N-1}$ skyrmions      225
$\theta$ -vacuum      208
1/N corrections      126
1/N expansion      49 109 124 267 280
1/N limits      26
Abelian bosonisation      241
action      39 150—152 163 178 182 184 185 191 192 266
Action-like variables      168
Addition of a uniton      132
Angular momentum operator      237
Anharmonic potential      44
Anomaly      199 201 206—208 215 223
Anomaly-free representation      200
Anti-instanton      32 35 48 69 225
Anti-instanton solution      13
Antibasic unitons      133
Anticommutation relations      6 41 42 256
Anticommuting fields      37
Anticommuting quantities      6 20 49
Anticommuting variables      40
Antiholomorphic vector      140
Antiself-duality      47 48 52 53
Associated Dirac problem      86
Associated Dirac-like background problem      72 106 162
asymptotic freedom      49 120
Atiyah — Singer index theorem      266
Axial current      201
Axial nonsinglet current      208
Axial vector current      202 205
Background field      99
Bare coupling constants      129
Basic uniton      133
Berezin integration      8
beta function      247
Bethe ansatz      263 264 267
Bianchi identity      47
Bogomolnyi-like bound      48
Boson-fermion equivalence      243
Bosonisation      241 257
boundary conditions      27 28
Canonical anticommutation relations      252
Canonical point transformations      16
Canonical quantisation      1 4
Cauchy — Riemann relations      61
Central charges      267
Changes of variables      14
Chern — Simons term      234
Chiral determinants      206
Chiral fermions      199 206 209 210
Chiral field      262 264
Chiral model      131 132 157 182 187 192 266
Chiral solutions      166
Classical equations of motion      132
Classical ground state      36
Classical solutions      33 46 94
Collective coordinates      34 76 92 218
Commutation relation      1
Completely integrable      168
Complex Grassmann manifold      50 51
Complex solutions      35
Composite models      129
Confinement of fermions      49
Conformal group in two dimensions      54
Conformal invariance      48 121 200 247 260
Conformal symmetry      249
Conformal transformation      54
Conservation laws      168 179 189 258 260
Conservation of energy momentum      56
Conserved currents      251
Constants of motion      168
Coset spaces      131
Covariant derivative      39 51 53 70
Critical phenomena      268
Current algebra      215 245 251 253 255
Curvature      259
Descent equations      211
Determinant      25 35 91 277
Dimensional regularisation      195 281
Dirac action      210
Dirac background problem      97 266
Dirac fermions      206
Dirac operator      44 99
Dirac quantisation condition      177
Dirac string      176
Double potential      36
Double well      30
Dynamical variables      40
Effective action      22 128
Effective potential      110
Energy-momentum tensor      56 247 249 255 256 260
Equations of motion      24 28 29 31 48 53 56 62 64 102 175 176 193 251
Evolution operator      1 2
extended objects      225
Extended solutions      224
Extended structures      162 233
Fermion      6 8 37 94 201 209
Fermionic current algebra      201
Fermionic determinant      44 264
Fermionic integration measure      202
Fermionisation      241
Feynman integrals      124
Feynman parametrisation      280
Feynman rules      124
Field theory      6 8 20 168
Finite action solutions      52 55 56 75
Fluctuation      88 152 159 162 278
Fluctuation determinant      75
Fluctuation operator      25 28 32 34 72 76 78 86 91 92 152 162 266
Fluctuation potential      89
Fluctuation spectrum      72
Fluctuations around the instanton solutions      75
Fock space      252
form factors      265
Fourier transforms      14
Fractional Hall effect      237
Fractional spin      233 237 238 268
Fujikawa method      204 205
Functional      14 6
Functional $\delta$ function      116
Functional derivative      11
Functional determinant      14 15 30 44 78 276 277
Functional differentiation      10
Functional gaussian      12 13 19
Functional integral      4 8 10 16 24 26 28 35 46 78
Functional integration      10 29 35 40 76
Functional measure      112
Functional trace      15
Gauge field      202 206 223 233 258
Gauge invariance      117 125—127 200 202 205—208 211 255
Gauge potential      233
Gauge symmetry      126 210
Gauge theories      210 265
Gauge transformations      255
Gaussian Integrals      124
General grassmannian models      63
Generalised curvature tensor      194
Generating functional      20 22 24 25 116 257
Generation of mass      120
Generation of the fermion mass      128
Geodesic motions      228
Gramm — Schmidt orthogonalisation      61 63
Gramm — Schmidt orthonormalisation      63
Grand unification      214
Grassmann algebra      6 7 104
Grassmannian      38 162 166 173 266
Grassmannian embeddings      157

Grassmannian field      131
Grassmannian models      46 49 50 52 94 133 135 148 150 152 168 170 187 224
Grassmannian projector      158
Grassmannian quantities      7
Grassmannian solutions      145 148 149 157 162 177 182
Green functions      20 21 25 29 75 79 80 111 123 126 277 278
Gross — Neveu model      263
Ground state      30 44
Ground state energy      29 110
Group manifold      131
harmonic oscillator      27 30 36 43
Hermitian conjugation      7
Hilbert — Riemann problem      170
Holomorphic bases      148
Holomorphic curve      102
Holomorphic matrix      135 146
Holomorphic projector      147
Holomorphic vector      103 140
Hopf term      233—238 268
Index theorem      99
Infrared divergences      126
Instability      157
Instanton      30 32—35 48 64 69 75 225
Instanton equation      228
Instanton quarks      86
Instanton solution      62 71 148 278
Instantonic embeddings      158
Integrability      170
Integrable      179
Integration operation for anticommuting variables      7
Interacting boson-fermion model      106
Kac — Moody algebra      245—247 249 251 255 256 268
Kahler like metric      227 231
Kahler manifold      103
Kahler metric      231 232
kinetic energy      226
Korteweg-de Vries equation      168
Lagrangian density      55 76 95 106 131 198
Lax equations      180
Lax formalism      179
Lax pair      170
Lax problem      170 173 175 177 179 189
Lax system      178
Left-handed fermions      210
Legendre transform      22
Levi — Civita connection      191 193 198
Lie algebra      245
Light-cone variables      260
Linear changes of variables      14
Linear coulomb potential      129
Linear potential      127
Local minima of the action      71
Lorentz force      176
Magnetic monopole      176
Majorana spinor      94
Mass gap      268
Massive Thirring model      241 263
Massless Dirac equation      251
Metric      195 197
Minimal coupling substitutions      223
Minimal uniton number      133
Mixtures of instantons and anti-instantons      61
Modified, KdV equation      169
Multilinear functional      10
Natural holomorphic normalisation      147 149 151
Negative fluctuation modes      187
Negative modes      86 92 152 155 159 162 178 266
Neveu — Schwarz field      252
Noether current      199 208
Nonabelian bosonisation      241 257 268
Nonabelian gauge theories      46 48 52 131
Nonabelian monopoles      225
Nondynamical variable      40
Nonembedding solutions      136
Nongrassmannian solutions      133 156 157
Noninstanton solutions      69 71 86 172 175 230
Nonlinear changes of variables      15
Nonlocal currents      258
Nonlocal interaction      114
Normal ordering      247 253
O(4) $\sigma$ model      131
O(N) $\sigma$ models      50
One-loop beta function      244
Operator ordering      4 19
Orthogonal holomorphic basis sequence      147 149
Parallelisable models      197
Parallelisibility      195
path integral      1 2 6 16 17 19 28 257 265
Pauli exclusion principle      6
Pauli matrices      131
Pauli — villars cut-off      119
Perturbation expansions      109
Perturbation theory      22 30 46 112 124
Phase space      2 6 19
Point splitting      256
Point-splitting regularisation      205
Poisson brackets      244 245
Projector      61 64 131 135 136 146 149—152 155 170 173 182 183
Quantisation      41
Quantum corrections      86 267
Quantum effects      43 121 124
Quantum gauge fields      224
quantum mechanics      1 27 109
Quark-field confinement      49
Regularisation      200 205 207 276
Renormalisability      195
Renormalisation      196 200 208 243
Renormalisation group      199
Renormalisation group invariant      85
Renormalised coupling constant      124
Riemann curvature tensor      191 232
Riemann zeta function      276 277
Right-handed fermions      210
Rotating soli ton      223
Running coupling constant      85
S matrix      263 265
Saddle-point condition      120 128
Saddle-point evaluation of integrals      22
Saddle-point method      24 27
Saddle-points of the action      86 266
Schwinger term      201 245 255—257
Self-dual solutions      135 163
Self-duality      47 48 52—54 102
Sigma model anomalies      209
Sigma models      258 265
Sine — Gordon model      241 263
Skyrme model      220
Skyrme term      216 224
Skyrmion      220 223 225 233—236 238 265 268
Small fluctuation      48 70
Soliton      219
Source current      200 202 207 208
Spherical tensors      89
Spontaneous symmetry breakdown      43
Stability properties      152
Stationary points of the action      24
String models      268
String theory      252
Superfields      39 197
Supergravity models      126
Superpotential      40
Superspace      38 39 94 102—104
Supersymmetric field theory      37
Supersymmetric field theory instantons      103 105
Supersymmetric field theory Lagrangian      106
Supersymmetric field theory quantum mechanics      37
Supersymmetric field theory theories      44
Supersymmetry      41 42 94 97 102 197 267
Supersymmetry generators      38
Supersymmetry transformation      38 39

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