Feynman-Kac formula associated with a system of partial differential operators
type: Item
instance of: scholarly article
title: Feynman-Kac formula associated with a system of partial differential operators
zbMATH Open document ID: 0603.28013
DOI: 10.1016/0022-1236(86)90009-1
author: Hiroshi Watanabe
published in: Journal of Functional Analysis
publication date: 1986-01-01T00:00:00Z
review text: The approach to Feynman path integrals, based on Fresnel integrals over a Hilbert space, put forward by \textit{S. A. Albeverio} and \textit{R. J. Hoegh- Krohn} [''Mathematical theory of Feynman path integrals'' (1976; Zbl 0337.28009)] is extended such as to allow one to obtain Feynman-Kac formulae for the fundamental solutions of a wider class of differential operators, including the Dirac operator with an external scalar potential. A difficulty related with the consistency of such a definition when extending it e.g. to the case of the Dirac equation with a vector potential is partially solved.
Mathematics Subject Classification ID: 28C20
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 81S40
Mathematics Subject Classification ID: 81Q05
zbMATH DE Number: 3973219
zbMATH Keywords: product integral
zbMATH Keywords: Feynman path integrals
zbMATH Keywords: Fresnel integrals over a Hilbert space
zbMATH Keywords: Feynman-Kac formulae
zbMATH Keywords: Dirac operator
reviewed by: Nicolae Angelescu
MaRDI profile type: Publication
full work available at URL: 0022-1236(86)90009-1
OpenAlex ID: W2077494431
cites work: Mathematical theory of Feynman path integrals
cites work: Space-Time Approach to Non-Relativistic Quantum Mechanics
cites work: A construction of the fundamental solution for the Schrödinger equation
cites work: Q5508009
cites work: Q3871260
cites work: A construction of the fundamental solution for the relativistic wave equation. I
cites work: Path integral for some systems of partial differential equations
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description: scientific article; zbMATH DE number 3973219