Discrete-time path distributions on a Hilbert space (Q1928397)

The problem of a mathematically rigorous definition of the Feynman path integral is considered. Different approaches to this problem are briefly reviewed. One of the latest approaches is due to \textit{E. G. F. Thomas} [Verh. Afd. Natuurkd., 1.\ Reeks, K. Ned. Akad. Wet. 52, 235--268 (2000; Zbl 0996.58013)] who suggested to define the path integral as a generalized type of distribution, in the spirit of De~Witt-Morette, which he called a path distribution. Thomas constructed an analogue of the path integral in discrete time, where the paths are sequences in a certain nuclear sequence space; his main idea was to define the path integral as a derivative of a specific measure. The authors of the present paper simplify this approach by defining the path distribution instead on a space of paths in a Hilbert space. This makes the construction more explicit and the technical details less demanding.