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Rivers R.J. — Path Integral Methods in Quantum Field Theory
Rivers R.J. — Path Integral Methods in Quantum Field Theory

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Название: Path Integral Methods in Quantum Field Theory

Автор: Rivers R.J.

Аннотация:

This is a concise graduate level introduction to analytical functional methods in quantum field theory. Functional integral methods provide relatively simple solutions to a wide range of problems in quantum field theory. After introducing the basic mathematical background, this book goes on to study applications and consequences of the formalism to the study of series expansions, measure, phase transitions, physics on spaces with nontrivial topologies, stochastic quantisation, fermions, QED, non-abelian gauge theories, symmetry breaking, the effective potential, finite temperature field theory, instantons and compositeness. Serious attention is paid to the shortcomings of the conventional formalism (e.g. problems of measure) as well as detailed appraisal of the ambiguities of series summation. This book will be of great use to graduate students in theoretical physics wishing to learn the use of functional integrals in quantum field theory. It will also be a useful reference for researchers in theoretical physics, especially those with an interest in experimental and theoretical particle physics and quantum field theory.


Язык: en

Рубрика: Физика/Квантовая теория поля/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1987

Количество страниц: 339

Добавлена в каталог: 27.09.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$CP^{N-1}$ model      318
$\Theta$-vacua      302 305
Aharanov — Bohm effect      140 144
Anomalous symmetry breaking      173 230
Arnowitt — Fickler gauge      see “Axial gauge asymptotic freedom”
Axial gauge      205 217 236
Axion      308
Background field quantisation      75 213
Becchi measure Rouet — Stora (BRS) identities      210
Bloch-wave vacuum      305 307
Block — Nordsieck approximation      187 192 328
Bogoliubov transformation      286
Boltzmann distribution      146
Boltzmann sum      82
Boltzmann weights      83
Borel summation      100
Borel uniqueness      101
Bose statistics      6
Bound states      see “Composite fields Brownian motion”
Broken symmetric vacuum      305 307
Cabibbo angle      234
Chiral symmetry      173
Classical action for $CP^{N-1}$ model      318
Classical action for complex scalar field      21 62 72
Classical action for fermion Yukawa theory      160 164
Classical action for Goldstone model      223
Classical action for Gross — Neveu model      320
Classical action for Higgs model      227
Classical action for non-linear sigma model      316
Classical action for QCD      202
Classical action for QED      180
Classical action for real scalar field      3 58
Classical action for Wess — Zumino model      168
Classical limit      30 82 224 250
Classical paths for bosons      82
Classical paths for fermions      176
Classical paths for instantons      293 298 299
Classical paths for particle on a ring      137
Coleman — Weinberg mechanism      243 271 290
Collective coordinates      96 295
Colour      200 217
Combinatorics      1
Complex scalar fields      20
Composite fields      309 310 316 317 319 329
Configuration space for non-Abelian gauge theory      307
Configuration space for particle on ring      141
Confinement in QCD      217 323
Connected Feynman diagrams      26
Connected Green functions      26
Coordinate transformations      123
correlation length      133
Coulomb gauge      202 207
Covariant gauges      183 206
CP violation      308
Critical behaviour of lattice field theory      133
Critical temperature      264 265 268 272
Curvilinear coordinates      123 135
Cylinder set      117
Degree of divergence      45
Dilute gas approximation for instantons      295 299 303
Dimensional regularisation      47 126 132
Dirac equation      160 161
Dyson — Schwinger equations for connected Green functions      27
Dyson — Schwinger equations for fermionic Green functions      163
Dyson — Schwinger equations for one-particle-irreducible Green functions      35
Dyson — Schwinger equations for scalar Green functions      8
Dyson — Wick expansion for fermionic fields      164
Dyson — Wick expansion for finite temperature      259 281
Dyson — Wick expansion for scalar field      14 63
Edwards — Gulyaev effect      124 202 207
Effective action      36 76
Effective action to one-loop      86
Effective action with fermions      172
Effective potential      37
Effective potential at finite temperature      260
Effective potential complexity      238 247
Effective potential complexity convexity      246 250 252 265
Effective potential complexity for gauge theories      239
Effective potential complexity to one-loop      86 237 249
Eikonal approximation      192
Electro weak unification      230
Electromagaetic field      180
Electron      180 232
Electron anomalous magnetic moment      99 145
Electron propagator      163 188 190
Elementary fields      1
Equal-time anticommutation relations (ETARs)      161
Equal-time commutation relations (ETCRs)      3
Equation of Fokker — Planck      148
Euclidean Feynman rules      44
Euclidean lattice theory      127
Euclidean stochastic quantisation      157
Euler-Lagrange equations      3
Expansions in 1/N      310 321
Expansions in coupling strengths      see “Feynman series”
Expansions in h      see “h-expansions”
Expansions in loops      see “Expansion loops”
External-field propagator for electron field      185 188
External-field propagator for scalar field      17 61 67 69
Fadeev — Popov determinant      204 207
False vacuum      293 297
Fermi statistics      160 161 166
Fermion field Green functions      161
fermions      159
Feynman diagrams      15
Feynman gauge      184
Feynman rules for Euclidean scalar theory      44
Feynman rules for fermion fields      164
Feynman rules for finite temperature (Euclidean) theory      257 260
Feynman rules for finite temperature (real time) theory      276 280
Feynman rules for scalar theory      42 64
Feynman series      10 63 66 102
Feynman series of rearrangement      102
Feynman series of summation      99
Feynman series of variationally improved summation      105
Field doubling at non-zero temperature      274 275 276
Finite temperature field theory      255 277
Finite temperature Green functions      256 280 283
First homotopy group      141
First order phase transitions      264 272
Fokker — Planck generating functional for scalar field      158
Fokker — Planck generating functional for zero-dimensional field      154
Free energy      260
Functional differentiation      4 162
Functional integration      58
Functional integration by lattices      127
Functional integration by measures      109 114
Functional integration by modes      110
Functional integration by time-slices (quantum mechanics)      79 122
Functional integration of a complex scalar field      72
Functional integration of a Euclidean scalar field      91
Functional integration of a real scalar field      63
Functional integration of fermion fields      173
Functional integration of Grassmann variables      177
Functional integration of the electromagnetic field (QED)      183
Functional integration of the gluon field (QCD)      204
Functional vacuum      24 307
Functionals      3
Fundamental group      see “First homotopy group”
Gauge fixing in QCD      202
Gauge fixing in QED      182
Gauge fixing in stochastic quantisation      196
Gauge invariance      181 184 192 204 236
Gauge transformations for Higgs model      228
Gauge transformations for QCD      201
Gauge transformations for QED      181
Generating functional normalisation      16 114
Generating functionals for $CP^{N-1}$ model      318
Generating functionals for background fields      75
Generating functionals for complex scalar fields      21
Generating functionals for connected Green functions      28
Generating functionals for Euclidean scalar fields      91
Generating functionals for external fields      17 60
Generating functionals for fermion Yukawa theories      165
Generating functionals for finite temperature fields (Euclidean)      258
Generating functionals for finite temperature fields (real time)      281
Generating functionals for free fermion fields      163
Generating functionals for lattice scalar theory      127
Generating functionals for non-linear sigma model      316
Generating functionals for one-particle-irreducible (1PI) Green functions      34
Generating functionals for QCD      204
Generating functionals for QED      183
Generating functionals for real scalar free fields      14 58
Generating functionals for Symanzik construction      6
Ghosts      205 206 208 273 281
Glashow — Salam — Weinberg (GSW) model      230 236 241 243 271
Gluons      2 199 217 309
Goldstone bosons (modes)      233
Goldstone bosons model      223
Goldstone's theorem      222
Grassmann variables      161 177
Grassmannian differentiation      162 177
Grassmannian integration      173 176
Gribov ambiguity      207 307
Gross — Neveu model      32
H-expansion      78
H-expansion of effective potential      246
H-expansion relation to coupling-constant expansion      93
Hamiltonian of Fokker — Planck      150 157
Hamilton’s equations      3
Hartree approximation      32 74 314
Heat bath      see “Thermal bath”
Heisenberg equations      2 161
Higgs mechanism      227 245
Higgs mechanism, mass      241
Higgs mechanism, particle      232 309
Hoelder index      119
Homotopic equivalence      140
In vacuum      39
Index-space notation for adjoint representation fields      322
Infrared divergences      187 265 267
instantons      289
Kubo — Martin — Schwinger relations      259 269
Lagrangian of Fokker — Planck      156
Landau gauge      184 197 240
Langevin equation for gauge fields      196
Langevin equation for scalar fields      151
Langevin equation for zero dimensions      149
Laplace expansion      88
Laplace’s method      90
Large-N limit      33 219 309
Large-N limit of $CP^{N-1}$ model      318
Large-N limit of Gross — Neveu model      320
Large-N limit of non-linear sigma model      316
Large-N limit of O(N) theory      310
Large-N limit of SU(N) gauge theories      323
Large-N planarity      321 323
Large-N planarity, N/JV expansion      310 321
Lattice field theory      127
Lattice field theory, leptons      2 230 233 309
Loop expansion for complex scalar field      73
Loop expansion for electron field      185
Loop expansion for real scalar field      66
Loop(h) expansion      see “h expansion”
Majorana field      160 168
Markov variable      146 198
Maxwell Gibbs construction      251
Mean-field approximation      32 74
Measure      109
Nambu — Jona — Lasinio model      320
Nicolai map      176
Non-Abelian gauge fields      199 203 228
Non-differentiable paths      114 119
Non-equilibrium processes      288
Non-linear sigma model      316
Non-zero temperature      see “Finite tempera”
One-particle-irreducible Feynman diagrams (1PI)      26
One-particle-irreducible Green functions      26
Ordering problems      125
Ornstein — Uhlenbeck process      118 120 152
Out vacuum      39
Particle on ring      136
Particle on ring in periodic potential      302
Particle on ring in potential well      292
path integral      59 109
Perturbation series in 1/N      321
Perturbation series in coupling strengths      see “Feynman series”
Perturbative renormalisation      48
Phase transitions      261 265 289
Phase-space integrals      78 178 257
Photon propagator      184 195 198
photons      181 184
Planar diagrams      323
Proper vertices      34
Pure states for non-zero temperature      275 285 288
QCD      see “Quantum cbromodynamics”
qed      see “Quantum electrodynamics”
Quantum chromodynamics      200 217 243 309 325
Quantum electrodynamics      180 199 202 203
quantum mechanics      89 306
Quarks      2 199 217 233 309
Quasi-interval      117
Rayleigh — Ritz variational method      32
Regularisation      12 41 45
Renormalisation      41
Renormalisation, coumerterms      52
Renormalisation, criteria      52
Renormalisation, group      53
Renormalised scalar coupling constant      50
Renormalised scalar coupling constant, scalar field      49
Renormalised scalar coupling constant, scalar mass      48
Rough paths      123 126
S-matrix      5 204
Saddle-point configurations for large-N      311 312 320 324 329
Saddle-point configurations for large-order      92 94
Saddle-point configurations for small-h      82
Saddle-point expansions      83 119 289 291 298
Scalar field Green functions      5
Schroedinger picture      24
Schwinger model      186
Second order phase transitions      264 266
Semi-classical (‘mean’) field      33 250
Series expansions      88
Series expansions for fermion theories      165
Series expansions for scalar theory      93
Series expansions for zero-dimensional theory      88
Series summation      99
Series summation, Borel summation      100
Series summation, fermi interference      169
Series summation, variationally improved summation      105
Simply connected spaces      141
Smoluchowski relation      115 148
Sobolev inequalities      94 97 98 134
Soft photons      189
Spontaneous symmetry breaking      220 235 255
State functionals      24 25 307
Static-ultra-local (SUL) model      12 22 74 128 155
Stationary-phase configurations      82
Stationary-phase configurations, expansions      83
Statistical disorder      261
Statistical disorder, order      261
Steepest descent      90
Stochastic Green functions      151 154
Stochastic quantisation      145
Stochastic quantisation and gauge fixing      195
Stochastic quantisation and supersymmetry      174
Stochastic quantisation and the Gribov ambiguity      208
Strong-coupling      74 192
Superficial degree of divergence      45
Supersymmetry      167 176
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