'feynman measure' 221 258 268 273
'feynman measure' cameron theorem 217 272
'feynman paths' 275 306—311 314
'integrity' see also “identity problem” 5 48
'turing paradox' see also “'zeno's paradox'” 96
'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 passim
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 passim
Approximative state space 42 passim
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 (c3) 60
Assumption (c4) 62
Assumption (cl, 2) 58
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 (ul, 2) unstable systems 6
Barrier gamow method 2 140 289 312
Barrier partially absorbing 173
Barrier-penetration decay 140 289 312
Baumgartel theorems 117 121 143
Beam-foil technique 3 47 51
Bochner — khintchin theorem 21 22
Bounded-energy approximation see also “energy filtering” 39—47 52
Bounded-energy state 40 passim
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 passim 208
Chamber 54ff
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 177 passim
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 3ff
Conjugation 163 164
Continual observation limit of see “limit”
Continual observation true 93 96
Continuous contractive semigroup 22ff 147ff 318—320 324 326 329 330
Convolution, of measures 222 passim 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
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 dynamical mechanism of 3 4 98ff. 139—141 143 144
Decay function 8 32 127
Decay law 8ff. 125 138
Decay law exponential 2 3 12 24 54 65 76 103
Decay law for a bounded-energy state 40
Decay law in presence of repeated measurements 53ff.
Decay law measured 58—60 65 66 69—72 76—78 81—84 95
Decay law 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 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 filtering 45 52 83 96 139 145
Energy resolution 83 193 194
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 sufficient conditions 31 32 51
Energy spectrum boundedness from below, necessary conditions 30 50
Energy spectrum relation to lifetime 38
Energy support 31 46
Enss condition 204
Euclidean invariance 131 145
Evolution equations see also “pseudo-hamiltonians”
Evolution equations in banch space 259—262 328
| Evolution equations non-linear 48 323;
Evolution operator see “propagator”
F-integral x 96 213ff.
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 see also “feynman — kac formula” 219 272
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 passim
F-integral gaussian-regularized see also “ito's method” 267 280 312
F-integral gaussian-regularized relation to fresnelian 267
F-integral in curved space 221 273
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 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-integral uniform product of time-dependent functions 284
F-integral with constraints 221 273
F-map 225ff.
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 passim
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 matrix for damped harmonic oscillator 293 passim
Frequency of measurement 62—65 70 71 81 95
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 passim
Fubini theorem 325
Function apparatus 306 passim
Function breit — wigner 2 9 33 78 96 112 136 139 150
Function decay 8 32 127
Function positive definite 17 passim
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 146ff. 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 passim
Hamiltonian phenomenological see “pseudo-hamiltonian”
Hamiltonian total 3 5ff.
Hamiltonian unperturbed 4 98ff.
Heat bath see reservoir
Holder continuous paths 240
Howland — baumgartel theorem 120 143
Identity problem, for unstable objects 3 55 138 145
Image-measure theorem 325
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 see also “unitary dilations” 17 40 45 46 50
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 inequality 168
Kato product formula 88 326
Kato smooth-perturbation theory 182 184 203 329
Kato theorem, on non-unitary wave operators 203
Kato — birman theory, for non-unitary scattering 201—203 211
Kinematical concept of unstable systems 4ff.
Kinematical concept of unstable systems postulates of 6ff.
Lee model 4 141
Lee — friedrichs model 141
Lidskii theorem 177 209
Lifetime see also “mean life” 9 38
Lifetime primary 72 passim
Limit classical 11 221 273 274 302—304 311
Limit non-damped, maslov correction 300—302
Limit of continual observation 84 passim 96 306 314—316
Limit of continual observation lack of operational meaning see also “'zeno's paradox'” 92 307
Limit of continual observation of position 93 94 96 311 314
Limit weak-coupling 48 140
Maslov correction 300—302 313
Maslov indices 269 275
Master equations, markovian 48
Mean life see also “lifetime” 9 92 136 138
Measurement frequency 62 65 70 71 81 95
Measures cameron theorem 217 272
Measures convolution of 222 passim 281
Measures gaussian 219 267 276
Measures set  222—224
Measures wiener 216 217 240 272 276 322
Memory effects 48 54
Method albeverio and hoegh — krohn 220 225 268 273 274 276 312
Method dewitt — morette 273 312
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