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| Exner P. — Open quantum systems and Feynman integrals |
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| Предметный указатель |
Method, Albeverio and Hoegh — Krohn 220 225 268 273 274 276 312
Method, DeWitt — Morette 273 312
Method, dilation-analytic 143 210
Method, Gamow 2 140 289 312
Method, geometric 142 212
Method, Ito 219 267 273 274 276
Method, Kato — Birman 201—203 211
Method, Tarski 273 276
Method, Weisskopf — Wigner 2 3 47 139 140
Minimality condition, embedded-eigenvalue perturbations 115
Minimality condition, unitary dilations 18
Misra and sinha, theorem on small-time regeneration 16 315
Model, damped harmonic oscillator 290—305 312
Model, Friedrichs 103—113 115 120 140 141 181 316 317
Model, kaons in a bubble chamber 71—76
Model, Lee 4 141
Model, optical 177 210
Naimark and Sz.-Nagy, construction 18—20 49 see
Naimark and Sz.-Nagy, theorem 17 49
Non-exponentiality of decay law 39 47 51 52
Non-exponentiality of decay law, large-time 33—36 51
Non-exponentiality of decay law, repeated measurements 54 66 77 see measured"
Non-exponentiality of decay law, small times 12—15 49 79
Non-unitarity of boosts 131 145
One-parameter semigroup 207 324 329
One-parameter semigroup, contractive see "Continuous contractive semigroup"
Open systems ix xiii 10 48 289
Open systems, ways of description 10—12 48
Operator of scalar type 210
Operator relatively compact 105 176 195 209
Operator, accretive 152 155 159 208
Operator, completely dissipative 157—159 175 197 208 209 319
Operator, dissipative 152
Operator, e.m.d. 155 165 167 170 174 175 203 208 209 290 319
Operator, J-selfadjoint 164 165 174 208 209 284
Operator, J-symmetric 163—165 174 208
Operator, maximal dissipative 154—159 164—169 173 195 198 208 209 292 309 318 319
Operator, maximal dissipative, extension problem 155 171—174 208 209 319
Operator, maximal symmetric 155 208 318
Operator, quasinilpotent 210
Operator, Schroedinger see "Schroedinger operator"
Operator, spectral 210
Operator, strictly accretive 159
Operators, compact 201
Operators, compact, singular values of 119 327
Operators, form sum 94 209 273 326
Operators, trace class 6 48 118 201 255 327
Optical approximation 179—194 210 211 320
Oscillator, anharmonic 313
Oscillator, damped harmonic 48 290—305 312 313
Oscillatory integrals 263 264 275 322
Paley — Wiener theorem 30 51 330
Partial wave decomposition 143 169—171
Partition 87 240
Partition, decomposition to subpartitions 241
Partition, generated by a subpartition 241
Partition, refinement of 241 243 265
Partition, regular 247
Partitions, commuting 241 243
Partitions, comparable 241
Partitions, crumbling sequence 247 265
Path integral, Feynman see "F-integral"
Path integral, Wiener see "W-integral"
Path space 214 222
Path space, Banach 239 248 269—271 322
Path space, Hilbert 222 234—240 243 245 270 273 274 322
Path space, Hilbert, euclidean motions of 231—233 267
Path space, Hilbert, reproducing kernel 239 274 321
Path sum 214 215 279
Path, dimension of 274 314
Path, Hoelder continuous 240
Path, Polygonal see "Polygonal path"
Perturbations of embedded eigenvalues 4 99 103—109 113—124 127—129 138—140 143 193 316 317
Perturbations of isolated eigenvalues 3 140 143
Perturbations of pseudo-hamiltonians 153 155 156 165—167 208 320
Perturbations of pseudo-Hamiltonians, relative bound 156 195 203 204
Perturbations, relatively compact 176
Perturbations, removing degeneracy in the first order 123
Phase shift 110 112 141 142
Phillips theorem on maximal dissipative operators 154 208
Photoemulsions 54 60 61
Poincare group 129
Poincare group, Casimir operators 130
Poincare group, Lie algebra of 130
Poincare group, representations of 5 6 130—136 144
Poincare group, representations of, for unstable elementary particles 4 132—136 144 145
Pole-and-real-axis approximation 103 107 129 139 140 151 177 316
Poles of reduced resolvent 101—103 107—109 113 121 123 127 138 141 142 316
Poles of scattering amplitude 110 141
Poles, higher-order 51 144 210
Poles, Puiseaux series 120—122 317 328
Polygonal paths 215 240—257 263—265 274—276
Polygonal paths, projections to 242
Positive definite function 17
Positive type see "Positive definite"
Postulates of kinematical concept 6
Potential for damped oscillator 290
Potential with below bounded real part 167 284
Potential, absorptive part of viii 175
Potential, almost regular 163
Potential, complex-valued 163
Potential, Feshbach optical 181 182 185 194 211
Potential, local 194
Potential, real-valued 171—174 257 312
Potential, Rollnik class 212
Potential, Saxon — Woods 194
Potential, spherically symmetric 169—173
Potential, strongly attractive 171—173 209 312
Potential, two-particle 166 284
Preparation theorem see "Weierstrass"
Prodistributions 273
Product formulae 257—262 275 285—289 325
Product formulae, Chernoff 326
Product formulae, Kato 88 326
Product formulae, Trotter 219 257 262 272 326
Product formulae, Trotter, generalizations of 262 326 327
Projection to polygonal paths 242
Projection, cylindrical 248 263
Propagator 5 98 159 259
Propagator in the limit of continual observation 86—91 94 306—311
Propagator of damped harmonic oscillator 292 303
Propagator, free 10 257
Propagator, reduced 7
Propagator, reduced, approximative 42
Propagator, reduced, energy support of 31
Propagator, reduced, the related positive-operator-valued measure 22 36—38 100—103 138
Propagator, unitary 159
Proton non-stability 2 97 126
Pseudo-hamiltonian x 12 146 278
Pseudo-hamiltonian of damped harmonic oscillator 290
Pseudo-Hamiltonian of damped harmonic oscillator, Maximal dissipativity 292
Pseudo-Hamiltonian, eigenvalues of 150 157 177 195 210 304
Pseudo-Hamiltonian, optical approximation 180—182
Pseudo-Hamiltonian, perturbations of 153 155 156 165—167 208 320
Pseudo-Hamiltonian, Schroedinger see "Schroedinger operator"
Pseudo-Hamiltonian, time-dependent 151 159—162 273
Puiseaux, cycles 120 124
Puiseaux, series 120—122 317 328
Quantization of dissipative systems 11 48 279
Quantization, F-integrals 221 273 276
Quasi-hamiltonian 149 207
R-matrix 110 111
Radiation damping 2 11 47 99 139
Radioactivity 2 47 92
Radon — Nikodym theorem 325
Realizability of infinite-energy states 14 15 47 49
Reduced resolvent 100
Reduced resolvent in friedrichs model 104—109 113 141
Reduced resolvent, poles of 101—103 107—109 113 121 123 138 141 142 316
| Reduced resolvent, poles of, residua 103 128 129 138
Regeneration 15 16 24 49
Relativistic invariance 4 5 129—139 144 145
Repeated measurements 8 53 138
Repeated measurements, density matrix 95 316
Repeated measurements, limit of continual observation see "Limit"
Repeated measurements, reproducing kernel 239 274 321
Reservoir 11 48 313
Resonance in friedrichs model 110—112
Resonance, definitions of 141 142
Resonance, dilation-analytic 142 143 352
Resonance, resolvent 142 see
Resonance, scattering 4 110 141 142 145 193
Riemann — Lebesgue lemma 25
Rollnik norm 203
S-matrix 110 111 179 204—207 212
S-matrix at energy  110
S-matrix, decomposability 110
S-matrix, non-unitary 204—207 212
S-matrix, optical 179
Scale-invariant, measurability 269 276
Scattering of neutrons on nuclei 177—179 181 191—194
Scattering, operator see "S-matrix"
Scattering, resonance 4 110 141 142 145 193
Scattering, theory 4 51 109—112 141
Scattering, theory, non-unitary 194—207 211 212
Scattering, theory, path-integral formulation 289 312
Schroedinger operator 10 219 278
Schroedinger operator, dissipative 165—177 194 203 204 208—210 212 279 319 320
Schroedinger operator, generalized 163 164 166 176 210
Schroedinger operator, generalized on a halfline 169—174 209
Schroedinger operator, strictly dissipative 175
Semigroup condition 3
Semigroup, completely non-unitary 157 197 330
Semigroup, continuous contractive 22 147 318—320 324 326 329 330
Semigroup, continuous contractive, generator of x 38 146 318—320 329
Semigroup, dynamical 48
Semigroup, holomorphic 89
Semigroup, unitary on a subspace 157
Sequential methods 263—266 275
Sequential methods, choice of approximation 263—265
Sequential methods, choice of limit 265
Simon theorem, on non-unitary wave operators 204 212
Sinha theorem, on permanent regeneration 24 26 50
Smooth perturbation technique see "Kato"
Smoothing, F-integrals 221 240
Smoothing, optical model 191—194 211
Sojourn time 10 48 142
Spark chamber see "chamber"
Spectral, concentration 99 140
Spectral, concentration in Friedrichs model 112 316
Spectral, singularities 209 210
Spectrum of damped oscillator 304
Spectrum, discrete 176
Spectrum, essential 176
Spectrum, Lidskii theorem 177 209
State 8
State space of an unstable system 5
State space of an unstable system, effective one-dimensionality for elementary particles 133—136
State space, approximative 42
State, bound 195—197
State, bounded-energy 40
State, decaying 195 196
State, eeduced 11 127 317
State, finite-energy 12 13 38 40 46 47 52
State, semibounded-energy 46 49
Subspace, absolutely continuous 28 50 110 116 150 179 195—207 211 321
Subspace, invariant under a semigroup 157
Subsystems, decay law of 126 127
Subsystems, non-interacting 126
Superselection rules 15 126 144
Symmetry 124 143
Symmetry of decay 125
Symmetry, broken 127
Symmetry, decomposition of a decay process 125—127
Symmetry, discrete 125
Symmetry, fynamical 125
Sz.-Nagy theorem, on continuous contractive semigroups 23 50
Tame function see "Cylindrical"
Technique, beam-foil 3 47 51
Technique, smooth-perturbation 182 184 203 329
Theorem, Baumgaertel 117 121 143
Theorem, Bochner — Khintchin 21 22
Theorem, Cameron 217 272
Theorem, Chernoff 49 326 327
Theorem, Davies 175 198 201 206 209 211 212 321
Theorem, Dirichlet — Jordan 330
Theorem, Ehrenfest 323
Theorem, Fubini 325
Theorem, Howland — Baumgartel 120 143
Theorem, image-measure 325
Theorem, Ito 267 276
Theorem, Kato 203
Theorem, Lidskii 177 209
Theorem, Misra — Sinha 16 315
Theorem, Naimark and Sz.-Nagy 17 49
Theorem, Paley-Wiener 30 51 330
Theorem, Phillips 154 208
Theorem, Preparation see "Weierstrass"
Theorem, Radon — Nikodym 325
Theorem, Riemann — Lebesgue lemma 25
Theorem, Simon 204 212
Theorem, Sinha 24 26 50
Theorem, Sz.-Nagy 23 50
Threshold effects 108 141 316
Time of arrival 93
Time, delay 48 142
Time, observable in quantum theory 48
Time, reversal 87
Translational invariance of 'feynman measure' 222 250
Translational invariance, decaying systems 131 145 318
Trotter product formula 219 257 272 326
Trotter product formula, uniform 262
Uniform-boundedness principle 324
Unitary dilations 17 49 330
Unitary dilations of a continuous contractive semigroup 24 36—38 147
Unitary dilations, application to unstable systems 18 20—22 50
Unitary dilations, construction in a finite-dimensional case 37
Unitary dilations, minimal 18 315
Unitary dilations, minimality condition 18
Unitary dilations, non-stability with respect to a parameter 38 40
Unstable system, bounded-energy approximation 39—47 52
Unstable system, connection to scattering theory 4 8 51 109—112 141
Unstable system, decay law see "Decay law"
Unstable system, observables 5 124 see
Unstable system, State space 5
Unstable systems x xiii 2
Unstable systems in quantum field theories 4 99 139—141
Unstable systems, identity problem 3 55 138 145
Unstable systems, kinematical concept 4 47
Virtual excitations 191
W-integral 215 222 233 240 252 274 275
W-integral, complex 274 275
W-integral, relation to F-maps 240 252 274 275
W-integral, sequential 275
Wannier ladder 140
Watchdog effect 96
Wave operators 109 198 321
Wave operators, completeness 110 204
Wave operators, generalized 355 321
Wave operators, non—unitary case 198—207 211 212 321
Weierstrass preparation theorem 327
Weisskopf — wigner method 2 3 47 139 140
Wiener integral see "W-integral"
Wiener measure 216 217 240 252 272 276 322
Wiener measure, dispersion of 216
Wiener sausages 314
Wiener spaces 239 274
Yes-no experiments 8 10 15 54 306
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