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arXiv · 2412.20643

Generating and Computing Quantum Periods in Exact WKB

Max Meynig
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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.

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Max Meynig. 2024-12-30. Generating and Computing Quantum Periods in Exact WKB. https://doi.org/10.1007/s11005-026-02099-z

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