Feynman-Kac formula associated with a system of partial differential operators
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.
scientific article; zbMATH DE number 3973219