Approximation of Feynman path integrals with non-smooth potentials

Abstract

We study the convergence in L2 of the time slicing approximation of Feynman path integrals under low regularity assumptions on the potential. Inspired by the custom in physics and chemistry, the approximate propagators considered here arise from a series expansion of the action. The results are ultimately based on function spaces, tools, and strategies which are typical of harmonic and time-frequency analysis.