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| Roepstorf G. — Path integral approach to quantum physics |
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| Предметный указатель |
Action at a distance 208
Action integral 83
Affine connection 303
Ahaxonov — Bohm effect 208
area law 310
Avogadro’s constant 4
Bernoullian random walk 6
Birman — Schwinger operator 127 207
Birman — Schwinger operator trace formula 130 207
Birman — Schwinger principle 127
Bispinor formalism 318—319
Bogoliubov inequality 191
Bogoliubov scalar product 191
Boltzmann weights 171
Boson field theory 217—224
Boson field theory, relation to quantum mechanics 231
Bosons (in solid states) 170
Bound states 126
Box — Muller algorithm 145
Brillouin function 254
Brillouin zone 9 13 179
Brownian bridge 110—112 180 357—358
Brownian bridge, Fourier decomposition 150
Brownian bridge, polygonal approximation 144
Brownian motion 7 21
Brownian motion, dynamical theory 33
Brownian motion, fractional 32
Brownian motion, law of iterated logarithm 182
Brownian motion, most probable path 109
Brownian particle 20 62
Brownian particle, life time 65
Brownian path 7 27
Brownian path, decomposition 111
Brownian path, Hoelder continuity 181
Brownian path, mean position 125
Brownian path, trail of a 8
Brownian tube 62
BRST symmetry 298
Canonical commutation relations 170 178 221
canonical ensemble 71
Chapman — Kolmogorov equation 5
Characteristic function of a measure 26
Charge conjugation 318
Choquard equation 186
Classical field 282
Classical field, connected with a quantum state 260
Classical filed 186
Classical limit 257
Coherent state 240
Compton wave length 249
condensate 223
Conditional expectation 29
Conjugate variables 262
continuum limit 13 179 244
Convexity 120 122 132 286
Cooper pairs 269
Correlation 75
Coulomb potential 50 119 121
Coupled systems 157
Covariance operator 227 358
Covariant derivative 289
Critical point 85
Cumulants 188
Curie point 268
Current (density) 283
Curvature 303
Cwickel — Lieb — Rosenbljum bound 132
Derivative (formal) 331
Diffusion constant 4 19
Diffusion equation 4 15
Dirac field 315
Dirac field, Euclidean 320—324
Dirac string 213
Dirichlet boundary condition 59 62 112
Double-slit experiment 17
Drift velocity 6
Dual pairs of spaces 229
DuHamel two-point function 189 191
Effective action 260—265
Effective potential 68 69 73 154 265—268
Effective potential, mean-field 273
Eigenvalues 62 66 127
Eigenvalues, asymptotic distribution 62
Eigenvalues, moment inequalities 135
electric field 48 161—169
entropy 252—255
Ergodicity 32
Euclidean action 230
Euclidean Bose field, path of the 228
Euclidean Bose field, statistical interpretation 218
Euclidean Bose field, stochastic interpretation 218 225
Euclidean momentum 220
Euclidean spacetime 216
Euler — Lagrange equations 89 106
Faddeev — Popov action 298
Faddeev — Popov determinant 294
Faddeev — Popov ghosts 296
Faddeev — Popov quantization 191
Fermion determinant 325
Fermion doubling problem 347
Ferromagnetic behavior 268
Ferromagnetic behavior, Curie — Weiss theory 274
Feynman function 220
Feynman integral 101
Feynman integral, radial 107
Feynman integral, sequential definition 102
Feynman — Kac formula 48—50
Feynman — Kac — Ito formula 198 210
Finite temperature fields 221
Fluctuation-dissipation connection 4
Flux quantization 213
Fourier expansion 161
Fourier transformation 9
Fourier — Laplace transform 339
Fractal set 7
Free energy 71 73
Free energy of a quantum field 259
Free energy, effective 186
Free field 76 238 264
Functional integrals 329—332
Functional integrals in QED 342
Galilean transformation 6 205
Gamma distribution 96
Gamma matrices 317
Gauge condition 285
Gauge fixing 283 286
Gauge fixing, axial gauge 292
Gauge fixing, Backgrond gauge 292
Gauge fixing, Coulomb gauge 292
Gauge fixing, Feynman gauge 288
Gauge fixing, Landau gauge 288 292
Gauge invariance 292 295
Gauge orbits 292
Gauge theory with fermions 346
Gauge theory, abelian 288
Gauge theory, nonabelian 289
Gauge theory, quantum chromodynamics 346
Gauge theory, Wilson approach 300
Gauge transformation 48 192 269
Gaussian density 14
Gaussian process 24 357
Gaussian process, generalized 226
Generating function 10
Ghost fields 297
Gibbs measure 230—231 242 252 256—258 305
Ginzburg — Landau equations 268—272
Golden — Thompson — Symanzik bound 67 175
Golden — Thompson — Symanzik bound, extension of the 160
Grassmann algebra 297 326
Green’s function 30 53 112 174 358
| Gribov ambiguity 298
Gribov copies 298
Gribov horizon 299
Ground state 37 58 60 74 77 88 100 146
Ground state, stochastic representation 58
Hamiltonian 48 50 171 178 190 192 207
Hamiltonian in field theory 236—238
Hamiltonian, time-dependent 47 159 160 175
Hard sphere gas 149
harmonic oscillator 37 67 174
Harmonic oscillator, driven 124 161
Harmonic oscillator, inverted 89
Harmonic oscillator, Mehler’s formula 37 57 60 77 88 89 124
Harmonic oscillator, partition function 37
Harmonic oscillator, perturbed 79
Harmonic oscillator, trace formula 90
Harmonic oscillator, transition amplitude 37
Harmonic spin chain 85 86
Heat equation 4
Heisenberg picture 75 174
Hida distribution 107
Hida distribution, S-transform of the 108
Hida distribution, T-transform of the 108
Higgs model 231 311—315
Homotopy 291
Increments of a process 27
Infrared divergence 12
instantons 232 291
Integral kernel of an operator 9
Integration (formal) 334
Ising model 274—278
Ito integral 195
Ito’s lemma 197
Jensen’s Inequality 67 80 118 126 360—360
Klein — Gordon equation 217
Kustaanheimo — Stiefel transformation 78
Landau diamagnetism 207
Landau free energy 269
Langevin equation 33
Laplace — DeMoivre theorem 4
Large deviations 185
Larmor frequency 206
Lattice 242 300
Lattice spacing 6 13 177
Lattice, dual 245
Lattice, Laplacian on a 245
Lattice, oriented links 300
Lattice, oriented plaquettes 304
Lebesgue theorem of bounded convergence 44 50
Levy algorithm 143 148
Lie algebra 289 300
Lie — Trotter product formula 56 103
Lieb’s formula 130—131
Loop variables 308
Lorentz manifold 285
Lyapunov exponents 141
Magnetic field 192 208 271
Magnetic field, constant 201—205
Magnetic field, Landau levels 270
Magnetic flux 208
magnetic moment 206
Magnetic phase 209
Markov chain 1
Markov process 23 92
Markov process, associated with a Hamiltonian 75
Markov process, transition probabilities 23
Mass matrix 61 69 81
Maxwell distribution 96
Maxwell field 282
Maxwell theory 281—286
Maxwell theory, Euclidean version 281
Mean field approximation 272—274
Mean square displacement 14
Measure space 20
Measure theory 20
Method of stationary phase 104
Min-max principle 127 137
Minkowski space 216
Minlos’s theorem 41
Monte Carlo method 142
O(4)-invariance 221 235
Observable 75
Open systems 159
Operator norm 51
Operator norm, norm convergence 56
Operator norm, stochastic representation 51
Order parameter 267
Ornstein — Uhlenbeck process 33 357—358
Ornstein — Uhlenbeck process, covariance operator 35
Oscillator bridge 165 175
Oscillator process 36 38 77 357—358
Oscillator process, covariance operator 36
Osterwalder — Schrader postulates 234—237
Parity transformation 317
Particle statistics 68 70 72
Partition function 71
Path integral, approximation 42
Path integral, basic concept 41
Path integral, integrable functions 43
Path integral, list of 362—367
Path integral, relation to Brownian motion 39
Path integral, several particles 61
Path integral, stochastic formulation 45
Path-ordered exponential 302
Pauli paramagnetism 207
Peierl’s argument 11
Perimeter law 310
Periodic boundary conditions 85
Perturbation expansion 79
Pfaffian 337
Phase space 68
Phase space, sum over histories 105
Phase transition 244 266
Phonons 170 177
Planck’s constant 15 68 110 255
Poisson statistics 167
Poisson summation formula 64
Polarization (dielectric) 189
Polarons 177
Polarons, effective mass 183
Polarons, field theory 186
Polarons, free energy 182
Polarons, Froehlich parameter 184
Polarons, Pecar’s result 185
Portenko’s lemma 52 54
Positivity preserving map 19
Probability measure 20
Quantized vortex 271
Quantum fluctuations 111 258 267
Quantum Hall effect 214
Quark fields 346
Quenched approximation 344
Random field 217
Random Fourier coefficients 150
Random potential 175 180
Random variable 20
Random variable, cumulants 79
Random variable, distribution 21 27
Random variable, distribution, joint 22
Random variable, expectation values 29
Random variable, Gaussian 21 34
Random variable, Gaussian, Wick power 38
Random variable, vector-valued 20
Random walk 1
Random walk on a lattice 6 249
Recurrence (random walk) 7 12
Reflection groups 91—94
Reflection groups of infinite order 94
Reflection positivity 234
Reflection principle 91
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