# Approximation of Feynman path integrals with non-smooth potentials

## TL;DR

This paper investigates the convergence of Feynman path integrals with non-smooth potentials using harmonic and time-frequency analysis, providing rigorous mathematical results under low regularity conditions.

## Contribution

It introduces a new approach to analyze the convergence of path integrals with low-regularity potentials using harmonic analysis techniques.

## Key findings

- Proves $L^2$ convergence of time slicing approximations
- Extends analysis to non-smooth potentials
- Utilizes harmonic and time-frequency analysis tools

## Abstract

We study the convergence in $L^2$ 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.