Remarks on low-energy approximations for Feynman path integration on the sphere

TL;DR

This paper discusses low-energy approximations for Feynman path integrals on the sphere, focusing on defining oscillatory integrals via action, Van Vleck determinant, and curvature, with convergence results for time slicing methods.

Contribution

It introduces a method using action integrals along shortest paths to approximate Feynman path integrals on the sphere, emphasizing low-energy functions.

Findings

Strong convergence of time slicing Feynman path integrals for low-energy functions

Definition of oscillatory integrals using action, Van Vleck determinant, and curvature

Method employs shortest paths for approximation

Abstract

We shall define the oscillatory integrals by action integrals, Van Vleck determinant and Dewitt curvature. Our method employs action integrals along the shortest paths. We have the strong but not uniform convergence of time slicing Feynman path integrals for low energy functions.