Generating and Computing Quantum Periods in Exact WKB
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866929744062185472 |
|---|---|
| author | Meynig, Max |
| author_facet | Meynig, Max |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20643 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generating and Computing Quantum Periods in Exact WKB Meynig, Max Mathematical Physics High Energy Physics - Theory 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. |
| title | Generating and Computing Quantum Periods in Exact WKB |
| topic | Mathematical Physics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2412.20643 |