Feynman integrals for non-smooth and rapidly growing potentials

TL;DR

This paper develops a framework for constructing Feynman integrals for the Schrödinger propagator involving highly singular and rapidly growing potentials, using white noise analysis, and demonstrates that these propagators can be expanded perturbatively.

Contribution

It introduces a novel approach to define Feynman integrals for complex potentials as generalized functions of white noise, extending the class of potentials for which the propagator can be constructed.

Findings

Feynman integrals are constructed for a broad class of singular and rapidly growing potentials.

All these propagators admit a perturbation expansion.

The method extends the applicability of Feynman integrals in quantum mechanics.

Abstract

The Feynman integral for the Schroedinger propagator is constructed as a generalized function of white noise, for a linear space of potentials spanned by measures and Laplace transforms of measures, i.e., locally singular as well as rapidly growing at infinity. Remarkably, all these propagators admit a perturbation expansion.