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| Exner P. — Open quantum systems and Feynman integrals |
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| Предметный указатель |
'feynman measure' 221 258 268 273
'Feynman measure', Cameron theorem 217 272
'feynman paths' 275 306—311 314
'integrity' 5 48 see
'turing paradox' 96 see
'zeno's paradox' 84—94 96 97 307 316
Absolutely continuous subspace 28 50 110 116 150 195—207 211 321
Accretivity 152 155 159 208
action 214 279 311
Albeverio and Hoegh-Krohn method 220 225 268 273 274 276 312
Algebra  222—234 251 252 254 256 263 264 266—270 275 279—281 322
Analytic continuation see "F-integral"
Anharmonic oscillator 313
Apparatus function 306
Approximation, bounded-energy 39—47 51
Approximation, optical 179—194 210 211 320
Approximation, pole-and-real-axis 103 107 129 139 140 151 177 316
Approximation, polygonal-path 215 240—257 263—265 274—276
Approximation, semibounded-energy 46
Approximation, semiclassical 273
Approximative, reduced propagator 42
Approximative, state space 42
Argument cook 199 211
Argument Cook, Haag and Kastler 46 52 139
Argument Cook, Von Schweidler 2 54
Assumption, (a), embedded-eigenvalue perturbations 116
Assumption, (a), Friedrichs model 105
Assumption, (a), non-unitary scattering 195
Assumption, (b), non-unitary scattering 205
Assumption, (b), optical approximation 179
Assumption, (c), non-unitary scattering 205
Assumption, (c), repeated measurements 56
Assumption, (c1,2) 58
Assumption, (c3) 60
Assumption, (c4) 62
Assumption, (D) 195
Assumption, (e) 205
Assumption, (f) 179
Assumption, (m) 115
Assumption, (n) 183
Assumption, (p1) 114
Assumption, (p2) 115
Assumption, (r) 55 138
Assumption, (s), non-unitary scattering 195
Assumption, (s), optical approximation 179
Assumption, (u) 190
Assumption, (u1,2), unstable systems 6
Barrier, Gamow method 2 140 289 312
Barrier, Partially absorbing 173
Barrier-penetration decay 140 289 312
Baumgaertel theorems 117 121 143
Beam-foil technique 3 47 51
Bochner — khintchin theorem 21 22
Bounded-energy, approximation 39—47 52 see
Bounded-energy, state 40
Breit — wigner function 2 9 33 78 96 112 136 139 150
Bubble chamber see "Chamber"
Cameron theorem, on non-existence of feynman measure 217 272
Cameron — Martin formula 233 254—257 267—269 275 313
Cayley transformation 153 208
Chamber 54
Chamber, bubble 54 60 76—84 92
Chamber, discrete 58 66—71 95
Chamber, homogeneous 62 63 71—76 95
Chamber, periodically structured 62—76 95
Chamber, spark 54 55 62 66—71
Chamber, structure of 55 56 58 60—65 71 76 77 79—81 95
Channels 111
Chernoff theorems 49 326 327
Classical limit 11 221 273 274 311
Classical limit, damped harmonic oscillator 302—304
Cogenerator 208
Compression 48
Condition, dissipativity 147 152
Condition, Enss 204
Condition, Friedrichs 104 111 113 114 121—123
Condition, minimality see "Minimality condition"
Condition, semigroup 3
Conjugation 163 164
Continual observation, limit of see "Limit"
Continual observation, true 93 96
Continuous contractive semigroup 22 147 318—320 324 326 329 330
Convolution, of measures 222 281
Cook argument 199 211
Coupling constant 3 104 140 143 177 316 317
Coupling constant, analyticity of pole positions 107 114 316
Coupling constant, Puiseaux series 120—122 317 328
Coupling constant, weak-coupling limit 48 140
CP-parity 3 129 144
CPT-invariance 87
Cylindrical, function 216 218 227
Cylindrical, function, basis of 227
Cylindrical, function, integration of 216 222 227 251 321
Cylindrical, projection 248 263
Cylindrical, set 216
Damped harmonic oscillator 48 290—305 312 313
Damped harmonic oscillator, 'ground state' 303 305
Damped harmonic oscillator, classical limit 302—304
Damped harmonic oscillator, non-damped limit 300—302
Damped harmonic oscillator, propagator of 292 303
Damped harmonic oscillator, pseudo-hamiltonian of 290—292
Damped harmonic oscillator, Pseudo-hamiltonian of, spectrum 304 305
Damped harmonic oscillator, ways of description 313
Damping, harmonic oscillator 48 290—305 312 313
Damping, radiation 2 11 47 99 139
Davies theorem on absolutely continuous subspace 198 211
Davies theorem on bijectivity of s-matrix 206 212
Davies theorem on completely dissipative schrodinger operators 175 209
Davies theorem on existence of  201 211 321
Decay function 8 32 127
Decay law 8 125 138
Decay law for a bounded-energy state 40
Decay law in presence of repeated measurements 53
Decay law, exponential 2 3 12 24 54 65 76 103
Decay law, measured 58—60 65 66 69—72 76—78 81—84 95
Decay law, measured, non-exponentiality see "Non-exponentiality of decay law"
Decay law, primary 56 65 66 70 72 76 78—80 85 93
Decay operator see "Decay function"
Decay rate, Fermi golden rule 3 107 108 122 139—141 143
Decay rate, initial 12—15 38 49 52 85
Decay rate, integral restrictions on 25 29
Decay rate, measured 65 69—72 76 85 95
Decay, dynamical mechanism of 3 4 98 139—141 143 144
Decay, Relativistic slow-down 77 136—138 145
Density matrix see "State"
Dewitt — Morette method 273 312
Dilation-analytic method 143 210
Dirichlet Laplacian 94 314
Dirichlet-Jordan theorem 330
Dissipative systems xiii 48 278
Dissipativity, (essentially) maximal see "Operator"
Dissipativity, complete 157—159 175 197 208 209 319
Dissipativity, condition 147 152
Dyson expansion 159—162 185—189 208 282 283
Effect, Stark 140 143
Effect, threshold 108 141 316
Effect, watchdog 96
Ehrenfest theorem 323
Eigenvector, generalized 195 210
Eisenbud — wigner formula 142
Energy spectrum, absolute continuity 28 51 178 195
Energy spectrum, boundedness from below 3 24 27 29—33 50 51 87 91
Energy spectrum, boundedness from below, necessary conditions 30 50
Energy spectrum, boundedness from below, sufficient conditions 31 32 51
Energy spectrum, relation to lifetime 38
Energy support 31 46
Energy, filtering 45 52 83 96 139 145
Energy, resolution 83 193 194
Enss condition 204
Euclidean invariance 131 145
| Evolution equations in Banach space 259—262 328
Evolution equations, non-linear 48 323 see
Evolution operator see "Propagator"
F-integral x 96 213
F-integral in curved space 221 273
F-integral of time-dependent functions 284
F-integral with constraints 221 273
F-integral, absence of dominated convergence theorem 233 321
F-integral, algebra 222—234 251 252 254 256 263 264 266—270 275 279—281 322
F-integral, analytic 269 280 313
F-integral, analytic continuation 218
F-integral, analytic continuation in mass 219 272
F-integral, analytic continuation in time 219 272 see
F-integral, analytic, relation to Fresnelian 269 270 273
F-integral, application to quantization 221 273 276
F-integral, Cameron — Martin formula 233 254—257 267—269 275 313
F-integral, change-of-variable transformations 230—233 253—257 322
F-integral, complex see "F-map"
F-integral, computer simulation 274
F-integral, discrete setting 274
F-integral, Fresnelian 225—234 251 266—270 273 274 279—283 313 321
F-integral, Fubini property 226
F-integral, Gaussian-regularized 267 280 312 see
F-integral, limiting 217 266 272 276 280
F-integral, limiting, relation to fresnelian 266
F-integral, notational convention 221
F-integral, operator-valued 271 277
F-integral, over histories 221 273
F-integral, phase-space 221 273
F-integral, polygonal-path approximations 215 240 257 263—265 274—276
F-integral, product 258 272 275 283 284 292 297—299 312
F-integral, regular cylindrical 249—257 275 312 313
F-integral, Relation to fresnelian 267
F-integral, relative to a form 268 276 313
F-integral, sequential methods 263—266 275
F-integral, uniform cylindrical 249—257 275
F-integral, uniform improperly cylindrical 249—257 275 280
F-integral, uniform product 258 284 292
F-map 225
F-map, change-of-variable transformations 230—233 253—257
F-map, Fresnelian 225—234 251 252 263 274
F-map, Fresnelian, extensions of 263 276
F-map, Fresnelian, generalized see "F-integral relative
F-map, product 258
F-map, regular cylindrical 249—257 275
F-map, relation to W-integral 240 252 274 275
F-map, uniform cylindrical 249—257 275
F-map, uniform product 258
Fci-formula 279 289 312
FCI-formula, anharmonic oscillator 313
FCI-formula, damped harmonic oscillator 292
FCI-formula, harmonic oscillator 313
FCI-formula, potential from  272 284
FCI-formula, potentials from  279
FCI-formula, potentials with below bounded real part 284
FCI-formula, relation to scattering theory 289 312
FCI-formula, time-dependent potentials 273 285
FCI-formula, two-particle potentials from  284
Fermi Golden Rule 3 107 108 122 139—141 143
Feshbach optical potential 181
Feshbach optical potential, Feynman — Cameron — Ito formula see "FCI-formula"
Feynman path integral see "F-integral"
Feynman — Kac formula 219 272 275 279 312
Feynman's thought experiment, with many-slit screens 214 307 313
Formula, Cameron — Martin 233 254—257 267—269 275 313
Formula, Eisenbud — Wigner 142
Formula, FCI see "FCI-formula"
Formula, Feynman — Kac 219 272 275 279 312
Formula, Fourier — Stieltjes inversion 30 324
Formula, product see "Product formulae"
Formula, Trotter 219 257 262 272 326
Fourier — Stieltjes inversion formulae 30 324
Free, Hamiltonian 10 163 178 179 195 208
Free, propagator 10 257
Frequency of measurement 62—65 70 71 81 95
Frequency, matrix for damped harmonic oscillator 293
Friedrichs, condition 104 111 113 114 121—123
Friedrichs, model 103—113 115 120 140 141 181 316
Friedrichs, model, multidimensional 113 141 317
Fubini, property 226
Fubini, theorem 325
Function, apparatus 306
Function, Breit — Wigner 2 9 33 78 96 112 136 139 150
Function, cylindrical see "Cylindrical function"
Function, decay 8 32 127
Function, positive definite 17
Gamow method 2 140 289 312
Gaussian measure 219 267 276
Gaussian measure, correlation operator 267 276
Gaussian measure, mean 267
Generalized, eigenvector 195 210
Generalized, observables 96
Generator of a semigroup x 38 146 318—320 329
Generators of Poincare algebra representation 130
Gisin equation 48 323
Haag — kastler argument 46 52 139
Hamiltonian, dual character of 147
Hamiltonian, free 10 163 178 179 195 208
Hamiltonian, of friedrichs model 104
Hamiltonian, phenomenological see "Pseudo — Hamiltonian"
Hamiltonian, total 3 5
Hamiltonian, unperturbed 4 98
Heat bath see "Reservoir"
Hoelder continuous paths 240
Howland — Baumgaertel theorem 120 143
Identity problem for unstable objects 3 55 138 145
Image-measure theorem 3 25
Integrals, Feynman path see "F-integral"
Integrals, improper 217 228 249 263—265
Integrals, oscillatory 263 264 275 322
Integrals, Wiener see "W-integral"
Interaction picture 162 185—187 282
Inverse decay problem 17 40 45 46 50 see
Ito, method 219 267 273 274 276
Ito, theorem 267 276
J-selfadjointness 164 165 174 208 209 284
J-symmetry 163—165 174 208
Jersak's equation 49
Joint system 126
Kaons, charged 76 79 144
Kaons, neutral 3 128 139 144 151
Kato — birman theory, for non-unitary scattering 201—203 211
Kato, inequality 168
Kato, product formula 88 326
Kato, smooth-perturbation theory 182 184 203 329
Kato, theorem, on non-unitary wave operators 203
Kinematical concept of unstable systems 4
Kinematical concept of unstable systems, Postulates of 6
Lee model 4 141
Lee — friedrichs model 141
Lidskii theorem 177 209
Lifetime 9 38 see
Lifetime, primary 72
Limit of continual observation 84 96 306 314—316
Limit of continual observation, lack of operational meaning 92 307 see
Limit of continual observation, of position 93 94 96 311 314
Limit, classical 11 221 273 274 302—304 311
Limit, non-damped, maslov correction 300—302
Limit, weak-coupling 48 140
Maslov, correction 300—302 313
Maslov, indices 269 275
Master equations, markovian 48
Mean life 9 92 136 138 see
Measurement frequency 62 65 70 71 81 95
Measures, Cameron theorem 217 272
Measures, convolution of 222 281
Measures, Gaussian 219 267 276
Measures, set  222—224
Measures, Wiener 216 217 240 272 276 322
Memory effects 48 54
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