Feynman-Kac formula associated with a system of partial differential operators

DOI10.1016/0022-1236(86)90009-1zbMath0603.28013OpenAlexW2077494431MaRDI QIDQ1082467

Hiroshi Watanabe

Publication date: 1986

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(86)90009-1

zbMATH Keywords

Dirac operatorFeynman path integralsproduct integralFeynman-Kac formulaeFresnel integrals over a Hilbert space

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Path integrals in quantum mechanics (81S40) Schrödinger operator, Schrödinger equation (35J10) Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.) (28C20)

Related Items

Stationary phase method in infinite dimensions by finite dimensional approximations: Applications to the Schrödinger equation, Functional integral and the Feynman-Kac formula in superspace, Path space measure for the 3+1-dimensional Dirac equation in momentum space, Feynman path integral for Dirac system with analytic potential, Feynman's formula in phase space for systems of pseudodifferential equations with analytic symbols

Cites Work

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• A construction of the fundamental solution for the Schrödinger equation
• Path integral for some systems of partial differential equations
• Mathematical theory of Feynman path integrals
• Space-Time Approach to Non-Relativistic Quantum Mechanics
• A construction of the fundamental solution for the relativistic wave equation. I