Exner P. — Open quantum systems and Feynman integrals :: Электронная библиотека попечительского совета мехмата МГУ

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Exner P. — Open quantum systems and Feynman integrals

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Название: Open quantum systems and Feynman integrals

Автор: Exner P.

Язык:

Рубрика: Физика/Квантовая механика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1985

Количество страниц: 356

Добавлена в каталог: 21.08.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

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 passim
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 passim 210
Naimark and sz.-nagy construction      see also “unitary dilations” 18—20 49
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      see also “decay rate measured” 54 66 77
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 accretive      152 155 159 208
Operator completely dissipative      157—159 175 197 208 209 319
Operator dissipative      152ff.
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 of scalar type      210
Operator quasinilpotent      210
Operator relatively compact      105 176 195 209
Operator Schrodinger      see “schrodinger 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 passim 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 240ff.
Partition decomposition to subpartitions      241
Partition generated by a subpartition      241
Partition refinement of      241 243 265
Partition regular      247 passim
Partitions commuting      241 243
Partitions comparable      241
Partitions crumbling sequence      247 265
Path dimension of      274 314
Path holder continuous      240
Path integral feynman      see “f-integral”
Path integral wiener      see “w-integral”
Path polygonal      see “polygonal path”
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
Perturbations of embedded eigenvalues      4 99 103 113—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 pole-and-real-axis approximation      103 107 129 139 140 151 177 316
Poincare group representations of      5 6 130—136 144
Poincare group representations of, for unstable elementary particles      4 132—136 144 145
Poles higher-order      51 144 210
Poles of reduced resolvent      101—103 107—109 113 121 123 127 138 141 142 316
Poles of scattering amplitude      110 141
Poles puiseaux series      120—122 317 328
Polygonal paths      215 240—257 263—265 274—276
Polygonal paths projections to      242 passim
Positive definite function      17 passim
Positive type      see “positive definite”
Postulates, of kinematical concept      6ff.
Potential absorptive part of      viii 175
Potential almost regular      163 passim
Potential complex-valued      163ff.
Potential feshbach optical      181 182 185 194 211
Potential for damped oscillator      290
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
Potential with below bounded real part      167 284
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 cylindrical      248 263
Projection to polygonal paths      242 passim
Propagator      5 98 159 259
Propagator free      10 257
Propagator in the limit of continual observation      86—91 94 306—311
Propagator of damped harmonic oscillator      292 303
Propagator reduced      7ff.
Propagator reduced approximative      42
Propagator reduced energy support of      31
Propagator reduced the related positive-operator-valued measure      22 passim 36—38 100—103 138
Propagator unitary      159
Proton non-stability      2 97 126
Pseudo-hamiltonian      x 12 146ff. 278ff.
Pseudo-hamiltonian eigenvalues of      150 157 177 195 210 304
Pseudo-hamiltonian maximal dissipativity      292
Pseudo-hamiltonian of damped harmonic oscillator      290
Pseudo-hamiltonian optical approximation      180—182
Pseudo-hamiltonian perturbations of      153 155 156 165—167 208 320
Pseudo-hamiltonian schrodinger      see “schrodinger operator”
Pseudo-hamiltonian time-dependent      151 159—162 273
Puiseaux cycles      120 124
Puiseaux series      120—122 317 328
Quantization f-integrals      221 273 276
Quantization of dissipative systems      11 48 279
Quasi-hamiltonian      149 passim 207
R-matrix      110 111
Radiation damping      2 11 47 99 139
Radioactivity      2 47 92
Radon — Nikodym theorem      325
Readability of infinite-energy states      14 15 47 49
Reduced resolvent      100ff.
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 is      16 24 49
Relativistic invariance      4 5 129—139 144 145
Repeated measurements      8 53ff. 138
Repeated measurements density matrix      95 316
Repeated measurements limit of continual observation      see “limit”
Reproducing kernel      239 274 321
Reservoir      11 48 313
Resonance definitions of      141 142
Resonance dilation-analytic      142 143 352
Resonance in friedrichs model      110—112
Resonance resolvent      see also “poles of reduced resolvent” 142
Resonance scattering      4 110 141 142 145 193
Riemann — Lebesgue lemma      25
Rollniknorm      203
S-matrix      110 111 179 204—207 212
S-matrix at energy $\lambda$ (on-shell)      110
S-matrix decomposability      110
S-matrix non-unitary      204—207 212
S-matrix optical      179 passim
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
Schrodinger operator      10 219ff. 278ff.
Schrodinger operator dissipative      165—177 194 203 204 208—210 212 279ff. 319 320
Schrodinger operator generalized      163 164 166 176 210
Schrodinger operator generalized on a halfline      169—174 209
Schrodinger operator strictly dissipative      175
Semigroup completely non-unitary      157 197 330
Semigroup condition      3ff.
Semigroup continuous contractive      22ff. 147ff. 318—320 324 326 329 330
Semigroup continuous contractive generator of      x 38 146ff. 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 discrete lidskii theorem      177 209
Spectrum essential      176
Spectrum of damped oscillator      304
Spectrum, discrete      176
State      8ff.
State bound      195—197
State bounded-energy      40 passim
State decaying      195 196
State finite-energy      12 13 38 40 46 47 52
State reduced      11 127 317
State semibounded-energy      46 49
State space approximative      42 passim
State space of an unstable system      5ff.
State space of an unstable system effective one-dimensionality for elementary particles      133—136
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 passim 143
Symmetry broken      127
Symmetry decomposition of a decay process      125—127
Symmetry discrete      125
Symmetry dynamical      125 passim
Symmetry of decay      125 passim
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 baumgartel      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 kato      203
Theorem lidskii      177 209
Theorem lto      267 276
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 delay      48 142
Time observable in quantum theory      48
Time of arrival      93
Time reversal      87
Translational invariance decaying systems      131 145 318
Translational invariance of 'feynman measure'      222 250
Trotter product formula      219 257 272 326
Trotter product formula uniform      262
Uniform-boundedness principle      324
Unitary dilations      17ff. 49 330
Unitary dilations application to unstable systems      18 20—22 50
Unitary dilations construction, in a finite-dimensional case3      7
Unitary dilations minimal      18ff. 315
Unitary dilations minimality condition      18 passim
Unitary dilations non-stability with respect to a parameter      38 40
Unitary dilations of a continuous contractive semigroup      24 36—38 147
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      see also “identity problem” 5 124
Unstable system state space      5ff.
Unstable systems      x xiii 2ff.
Unstable systems identity problem      3 55 138 145
Unstable systems in quantum field theories      4 99 139—141
Unstable systems kinematical concept      4ff. 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
Ways of description      313
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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