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| Albeverio S.A., Hoegh-Krohn R.J. — Mathematical theory of Feynman path integrals |
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| Предметный указатель |
Action, Hamilton's principle of least action 4 10
Analytic continuation, definition of Feynman integrals by 7 Ref.[10] 79
Analytic continuation, definition of Feynman integrals by of Wiener integrals 7 Ref.[10]
Anharmonic oscillator 11 46 65 78 118
Anharmonic oscillator, dynamics by Fresnel integrals 78 79
Anharmonic oscillator, expectations with respect to Gibbs state of harmonic oscillator 86
Anharmonic oscillator, expectations with respect to ground state of harmonic oscillator 80
Anharmonic oscillator, Feynman — Ito formula, small times 47
Anharmonic oscillator, Fresnel integrals, small times 47
Anharmonic oscillator, solutions of Schroedinger equation by Fresnel integrals 72 74
Annihilation-creation operators 90 91
Automorphisms of Weyl algebra 89 93 95 97 102 103 107 108 109 113
Banach function algebra, over  16
Banach function algebra, over  18
Banach function algebra, over D* 50
Bose fields 10 12 105—114
Brownian motion 7 9
Causal popagator 119
Classical action 10 26 31 80 90 99 105 109
Classical limit 7 8 Ref.[41]
Commutation relations 88 91 92
Complex measure 8
Complex potential 118
Composition, with entire functions 17 18
Cyclic vector 94
Euclidean — Markov fields 11
Euler — Lagrange equations 4
Expectations, for anharmonic oscillator 78
Expectations, for relativistic quantum Bose fields 105—114
Expectations, with respect to Gibbs state of the harmonic oscillator 86 89
Expectations, with respect to ground state of the harmonic oscillator 80 89 101
Expectations, with respect to invariant quasi free states 103—104
Exponential interactions 11 112—114
Feynman history integrals, as Fresnel integrals relative to a quadratic form 105—114
Feynman history integrals, heuristic 10—11
Feynman path integrals, as Fresnel integrals, anharmonic oscillators 65—89
Feynman path integrals, as Fresnel integrals, anharmonic oscillators, small times 46 47
Feynman path integrals, as Fresnel integrals, infinitely many harmonic oscillators 90—104
Feynman path integrals, as Fresnel integrals, non relativistic quantum mechanics 26—45
Feynman path integrals, as Fresnel integrals, relativistic quantum fields 105—114
Feynman path integrals, as Fresnel integrals, scattering operator 42—45
Feynman path integrals, as Fresnel integrals, solutions of Schroedinger equation 26—32
Feynman path integrals, as Fresnel integrals, wave operators 32—41
Feynman path integrals, definition by "analytic continuation" 7 Ref.[10] 79
Feynman path integrals, definition by "sequential limit" 7 Ref.[11]
Feynman path integrals, other definitions 7 9 23—25
Feynman — Ito formula 26 30 31
Feynman — Kac formula 7 26
Fields see "Bose fields"
Finitely based function 18
Fock representation 91 92 104 110
Free Boson field 105
Fresnel integrable, on 14—17
Fresnel integrable, on a real Hilbert space 18
Fresnel integrals, computations of 26—32 35—41 68 76 83 85—88 102—104 110—111 114
Fresnel integrals, for anharmonic oscillators, applications 65—114
| Fresnel integrals, for anharmonic oscillators, projectics 50—64
Fresnel integrals, for anharmonic oscillators, relative to a non degenerate quadratic form, definition 48—50
Fresnel integrals, for anharmonic oscillators, small times 46—47
Fresnel integrals, in non relativistic quantum mechanics (potential scattering) 26—45
Fresnel integrals, on a real separable Banach space 60—64
Fresnel integrals, on a real separable Hilbert space, definition 17—18
Fresnel integrals, on a real separable Hilbert space, properties 18—25
Fubini theorem, for Fresnel integrals on real Hilbert space 21—23
Fubini theorem, for Fresnel integrals on real separable Banach space 62
Fubini theorem, for Fresnel integrals relative to a quadratic form 53—64
Gaussian measure 24
Gentle perturbations 37
Gibbs states 12 104
Green's function 28 67 75
Hamilton's principle 4 10
Harmonic oscillator, finitely many degrees of freedom 90—90
Harmonic oscillator, infinitely many degrees of freedom 90—104 105—114
Heat equation 6
Homogeneous boundary conditions, transformation to 65
Improper normalized integral 36 41
Indefinite metric 24
Initial value problem 26
Integrals see "Feynman integrals" "Fresnel
Integration in function spaces 11
Invariance, Fresnel integral, under nearly isometric transformations 24
Invariance, orthogonal, for normalized integral 19—21
Invariance, translation, for normalized integral 15 19—21
Invariance, translation, for normalized integral with respect to quadratic form 53 73
Invariant quasi free state 93
Ito's functional 23
Models of quantum fields 11—12 111—114
Non relativistic quantum mechanics 1—9 26—45 65—104
Normalization 14
Normalized integral see "Fresnel integral"
Oscillatory integrals see "Fresnel integrals" "Feynman "Feynman
Parseval relation 18 24
Path integrals see "Feynman integrals" "Wiener
Polynomial interactions 11
Potential scattering 26—45
Quantum mechanics, non relativistic 26—45 65—104
Quantum mechanics, relativistic 105—114
Quantum mechanics, statistical 86—89
Quasi free states 90 93 97 103 108 113
Scattering amplitude, scattering operator 42
Schroedinger equation, solutions given by Fresnel integrals 26—32 65—74
Semigroup 79
Series expansions 27—45 68—79 85—89 114
Sine-Gordon interactions 112
State, on Weyl algebra 88—112
Stochastic field theory 12
Stochastic mechanics 9
Symplectic space 95 97
Symplectic transformation 95 97 108
Time ordered vacuum expectation values 10
Wave operators 32—42 44
Weyl algebra 88 92 102 107 109
Wiener measure 7 9
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