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| Masujima M. — Path integral quantization and stochastic quantization |
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| Предметный указатель |
Kinoshita, T. 101
Klauder, J.R. 102
Klein, A. 171
Klein, O. 170
Kolmogoroff, consistency condition 209 217
Kolmogoroff, existence theorem 209 217
Kugo, T. 169
Lagrangian 3 8 37 41
Lagrangian density, canonical locally G invariant 126
Lagrangian density, complex scalar 125
Lagrangian density, Dirac 124
Lagrangian density, effective 55 57 65 135 161
Lagrangian density, effective interaction 136
Lagrangian density, effective interaction, axial gauge 139
Lagrangian density, effective interaction, covariant gauge 144
Lagrangian density, effective interaction, Landau gauge 141
Lagrangian density, effective, R-gauge 162
Lagrangian density, Euclidean 185 199
Lagrangian density, Faddeev — Popov ghost 104
Lagrangian density, Faddeev — Popov ghost, axial gauge 138
Lagrangian density, Faddeev — Popov ghost, R-gauge 162
Lagrangian density, free 157
Lagrangian density, gauge field 103 115
Lagrangian density, gauged matter field 118
Lagrangian density, gravitational field 173
Lagrangian density, interaction 68 72 114 115 119 183
Lagrangian density, matter field 103 105 113 117 118 154
Lagrangian density, matter field, globally G invariant 151
Lagrangian density, modified Euclidean 177 181
Lagrangian density, modified Minkowskian 180
Lagrangian density, most general renormalizable 126
Lagrangian density, Non-Abelian gauge field 119
Lagrangian density, nonsingular 128
Lagrangian density, original 55
Lagrangian density, real scalar 125
Lagrangian density, total 67 113 115 119 154 156 159 161
Lagrangian density, total effective 105 106
Lagrangian density, total effective, R-gauge 151
Lagrangian density, ungauged matter field 118
Lagrangian formalism, analytical mechanics and quantum mechanics 1
Lagrangian formalism, quantum statistical mechanics 175
Lagrangian, effective 2 22 40 41 50
Lagrangian, Euclidean 176
Lagrangian, nonsingular 5 56 91 99
Lagrangian, singular 3 67
Landau, L.D. 51 52
Leader, E. 169
Lee, B.W. 100 168—173 273
Lee, T.D. 54
Legendre transform 4
Leschke, H. 206
Leutwyler, H. 170
Lie algebra 111
Lie algebra, semisimple 111
Lie group 104 107 108
Lie group, compact 107 108
Lie group, semisimple 104 107
Lifshitz, E.M. 51 52
Linked cluster expansion 184
Low, F.E. 173
Lurie, D. 52 171 205 273
Markov process 217 219
Matrix mechanics 1
Matsubara Green function 205
Matsubara representation 175 184 200
Matsubara, T. 205
Matsumoto, H. 171
Matthews, P.T. 101
McClain, B. 241
Meets, K. 100
Metric tensor, Minkowski space-time 57
Mid-point rule 2 16 40 42
Mills, R.L. 170
Minlos, R.A. 100
Mizrahi, M.M. 54
Momentum integration 35
Momentum integration, quasi-Gaussian integral 36 50 62
Morrison, D.F. 273
Muhlschlegel, B. 206
Multivariate Normal Analysis 106 269
Nakagoshi, H. 240
Nambu — Goldstone boson 105 106 150 151 154 155 157
Nambu — Goldstone boson, projection operator 164
Nambu — Goldstone direction 155
Nambu, Y. 101 170 171
Namiki, M. 240 241
Natural unit system 57
Neutral ps-ps coupling 80
Niemi, A. 241
Nishijima, K. 52 100
Normal dependence 3
Normal dependent 59
Operator ordering problem 2
Orbit, gauge equivalent class 104 129
Orbit, volume 104 128 129
Ornstein — Uhlenbeck process 241
Papadopoulos, G. 206
Parisi — Wu equation 222 223 240
Parisi — Wu equation, Abelian gauge field 230
Parisi — Wu equation, Non-Abelian gauge field 233
Parisi — Wu equation, Non-Abelian gauge field, covariant non-holonomic gauge fixing condition 237
Parisi, G. 205 240
Partition function, canonical ensemble 175 176 179
Partition function, canonical ensemble and grand canonical ensemble 176
Partition function, grand canonical ensemble 175 177 181 184
Partition function, grand canonical ensemble, functional differential equation 175 188
Parzan, E. 240
Path integral formula, Cartesian coordinate system 43
Path integral formula, configuration space 2 22 35
Path integral formula, configuration space, generating functional of Green’s function 38 64
Path integral formula, configuration space, matrix element of the operator 38
Path integral formula, configuration space, matrix element of the time-ordered product 37 63
Path integral formula, configuration space, transformation function 37 63
Path integral formula, curvilinear coordinate system 40 45
Path integral formula, Feynman 2 13 40
Path integral formula, phase space 2 22 28
Path integral quantization 20
Path integral quantization and canonical quantization 91
Path integral quantization, configuration space 55
Path integral quantization, configuration space, field theory 57 62
Path integral quantization, Feynman and Dirac 1
Path integral quantization, field theory 55
Path integral quantization, gauge field 103 104 127
Path integral quantization, gauge field, Faddeev — Popov method 104 106 128
Path integral quantization, gauge field, naive Feynman method 104
Path integral quantization, gauge field, R-gauge 106 158 171
Path integral quantization, gravitational field, Faddeev — Popov method 174
Path integral quantization, Lagrangian formalism 22
Path integral quantization, phase space 55
Path integral quantization, phase space, field theory 57 59
Path integral quantization, relativistic field theory 56
Path integral representation, configuration space 35
Path integral representation, configuration space, quantum field theory 62
Path integral representation, Feynman 13
Path integral representation, generating functional 73
Path integral representation, generating functional, Green’s function 55
Path integral representation, generating functional, temperature Green function 177
Path integral representation, Hamiltonian formalism 22
Path integral representation, partition function, canonical ensemble 175 176
Path integral representation, partition function, grand canonical ensemble 175 177 184
Path integral representation, partition function, interacting boson-fermion system 185
Path integral representation, phase space 27
Path integral representation, phase space, generating functional of the Green’s function 61
Path integral representation, phase space, matrix element of the time- ordered product 27 60
Path integral representation, phase space, transformation function 25 26 60
Path integral representation, quantum field theory 55
Path integral representation, quantum mechanics 1 55
Path integral representation, quantum statistical mechanics 175
Path integral representation, transition probability 223
Path integral representation, transition probability, stochastic quantization 223
| Path integral symbol 21
Path integral symbol, phase space 27
Path, arbitrary 8 14
Path, classical 8 13 14
Path, quantum 273
Peierls, R.E. 100
Perturbation theory, covariant 55 56 67 90
Perturbation theory, non-relativistic 54
Picture, Heisenberg 23 73
Picture, interaction 67
Picture, Schrodinger 24
Poisson bracket 3
Polaron problem 176 206
Politzer, H.D. 173
Polkinghorne, J.C. 101
Popov, V.N. 52 170 174
Potential, effective 2 40 48 55
Predazzi, E. 169
Principle of superposition 1 2 14 20 22
Probability amplitude, associated with the path 20 21
Probability space 212 216 217
Prokhorov, L.V. 54
Proper self-energy part 56 83 87
Quadratic form, canonically conjugate momentum 2 35
Quantum analog 11 12
quantum mechanics 1
Quantum mechanics, Hamiltonian formalism 2 23
Quantum mechanics, Lagrangian formalism 1 3
Quasi-Gaussian integral 2 18
Quigg, C 169
Ramond, P. 52 273
Revzen, M. 205
Ritz combination principle 1
Rosenfelder, R. 206 207
Ross, G.G. 169 173
Rotating coordinate 23 24
Rouet, A. 172
Sakurai, J.J. 52 170
Salam, A. 101 171 172
Sanda, A.I. 171
Scalapino, D.J. 206
Schiff, L.I. 51
Schreiber, A.W. 207
Schrodinger 1
Schrodinger equation 1 24
Schrodinger equation, imaginary time 176
Schrodinger equation, time-dependent 2 16 18
Schulman, L.S. 53
Schweber, S.S. 101
Schwinger mechanism 171
Schwinger theory of Green’s function 83 100
Schwinger — Dyson equation 56 83 90 175 194 195
Schwinger, J. 100 101 171 172
Sherrington, D. 206
Shirkov, D.V. 52 101
Simon, B. 53
Skagerstam, B.S. 102
Slavnov, A.A. 169 170
Spinor, Dirac 68 261
Spinor, indices 87 198
Spinor, Minkowskian, Euclidean 267
Spinor, relativistic 184
Spontaneous symmetry breaking 150
Stability group of the vacuum 152
State vector, time-dependent 24
State vector, time-independent 24
Stationary solution, Fokker — Planck equation 240
Stationary solution, Fokker — Planck equation, Non-Abelian gauge field 239
Stationary solution, Fokker — Planck equation, quantum field theory (nonsingular system) 230
Stationary solution, Fokker — Planck equation, quantum mechanics 229
Steiner, F. 54
Stochastic process 209 210 216 217
Stochastic quantization 209 240
Stochastic quantization, Abelian and Non-Abelian gauge field 223 230
Stochastic quantization, dynamical system, holonomic constraints 241
Stochastic quantization, Fermion 240
Stochastic quantization, Non-Abelian gauge field 223
Stochastic quantization, Non-Abelian gauge field, covariant non-holonomic gauge fixing condition 235
Stochastic quantization, Non-Abelian gauge-field, covariant non-holonomic gauge fixing condition 240
Stochastic quantization, six-dimensional space-time 241
Stora, R. 172
Stratonovich — Hubbard identity 204
Stratonovich, R.L. 206
Suger, R.L. 206
Svartholm, N. 172
Symanzik construction 55 72 73 100
Symanzik, K. 100
t Hooft, G. 172
Tachiki, M. 171
Taylor, C 241
Taylor, H.M. 240
Taylor, J.C. 169
Termini, S. 101
Third quantization, Nambu 101
Time-ordered product, matrix element of 2 15 22 27
Tomonager — Schwinger equation 67 73
Tonin, M. 101
Transformation function 1 2 8 10 12
Transformation law, gauge field 104
Transformation law, global G 122
Transformation law, global U(l) 122
Transformation law, Non-Abelian gauge field, finite 121
Transformation law, Non-Abelian gauge field, infinitesimal 118
Transformation law, U(l) gauge field 115
Transformation, canonical 5
Transformation, contact 1 3 6 8
Transformation, contact, analytical mechanics 6 10
Transformation, contact, infinitesimal 1
Transformation, contact, quantum analog 6
Transformation, contact, quantum mechanics 7
Transformation, coordinate 2 40 47 48
Transformation, gauge, finite 120
Transformation, gauge, linear 103 105 129 130 132 159
Transformation, gauge, nonlinear 134 146 155 160 167 168
Transformation, global G 117 122 151
Transformation, global phase 103
Transformation, global U(l) 114 122
Transformation, local 10-parameter Poincare 173
Transformation, local G 119 126 127 150 156
Transformation, local G phase 118
Transformation, local G, finite 120
Transformation, local G, infinitesimal 123
Transformation, local phase 103—105 155
Transformation, local U(l) 113
Transformation, local U(l) phase 113 115
Transformation, Stratonovich — Hubbard 176 201
Transformation, Weyl 48
Transition probability amplitude 1 2 14 22
Treiman, S.B. 102
Tyutin, I.V. 170 172
Umezawa, H. 101 171
Unification, electrostrong with Schwinger mechanism 172
Unification, electroweak with Higgs — Kibble mechanism 172
Unification, electroweak without Higgs — Kibble mechanism 172
Unification, Grand 173
Unitarity 105 127 128 133 210 236
Utiyama, R, 170 173
Vacuum expectation value 62
Vacuum expectation value, time-ordered product 31
Vacuum to vacuum transition amplitude 80
Varadhan, S.R.S. 206
Vassiliev, A.N. 52 101
Veltman, M. 172
Vertex operator 56 83 87 89
Visconti, A. 101
Walecka, J.D. 51 52 205
Ward — Takahashi — Slavnov — Taylor Identity 146 147 167
Ward, J.C. 172
Watanabe, T. 100
Wave function 17
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