Generating and Computing Quantum Periods in Exact WKB
Abstract
Periods of rational integrals appear in quantum mechanics through asymptotic expansions of traces computed with the semiclassical symbol calculus. We develop a novel formal series expansion for the trace of the Dirac delta of a differential operator. Restricting to operators which arise as the quantizations of polynomials, we are able to apply the Griffiths-Dwork reduction to the integrals. By developing this perspective, we find the reduction of all integrals in the asymptotic series to normal form through a finite calculation. In the case of one degree of freedom, the two dimensional residue formula relates the rational integrals to the quantum actions in the exact WKB formalism.
Cite
@article{arxiv.2412.20643,
title = {Generating and Computing Quantum Periods in Exact WKB},
author = {Max Meynig},
journal= {arXiv preprint arXiv:2412.20643},
year = {2025}
}
Comments
Includes minor updates and corrections to version 1. Comments are welcome