Oscillatory integrals on Hilbert spaces and Schrödinger equation with magnetic fields

DOI10.1063/1.531105zbMath0878.46034OpenAlexW2055533627MaRDI QIDQ4871954

Zdzisław Brzeźniak, Sergio A. Albeverio

Publication date: 19 May 1996

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.531105

zbMATH Keywords

Schrödinger equationoscillatory integralsCameron-Martins spacemathematical version of Feynman path integralsRamer's functional

Mathematics Subject Classification ID

Path integrals in quantum mechanics (81S40) Measures and integration on abstract linear spaces (46G12) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20)

Related Items (11)

ON CONVERGENCE OF THE FEYNMAN PATH INTEGRAL FORMULATED THROUGH BROKEN LINE PATHS ⋮ Feynman path integrals as infinite-dimensional oscillatory integrals: Some new developments ⋮ Phase space Feynman path integrals ⋮ A rigorous mathematical construction of Feynman path integrals for the Schrödinger equation with magnetic field ⋮ Stochastic Wess-Zumino-Witten model over a symplectic manifold ⋮ Mathematical theory of Feynman path integrals ⋮ CHERN–SIMONS THEORY, HIDA DISTRIBUTIONS, AND STATE MODELS ⋮ Generalized Fresnel integrals ⋮ Feynman path integrals for polynomially growing potentials ⋮ AN ANALYTIC APPROACH TO TURAEV'S SHADOW INVARIANT ⋮ Change of variable formulas for Feynman pseudomeasures

Cites Work

• The method of stationary phase for oscillatory integrals on Hilbert spaces
• Notes on the Feynman integral. III: The Schrödinger equation
• Feynman path integrals as infinite-dimensional oscillatory integrals: Some new developments
• On nonlinear transformations of Gaussian measures
• Finite dimensional approximation approach to oscillatory integrals and stationary phase in infinite dimensions
• Space-Time Approach to Non-Relativistic Quantum Mechanics
• Radon-Nikodym Derivatives of Gaussian Measures

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