Multiple Mellin-Barnes integrals in Schwinger-DeWitt technique
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911621276762112 |
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| author | Barvinsky, A. O. Kalugin, A. E. Wachowski, W. |
| author_facet | Barvinsky, A. O. Kalugin, A. E. Wachowski, W. |
| contents | We consider off-diagonal asymptotic series for integral kernels of functions of Laplace-type operators on curved backgrounds. These expansions are obtained by applying integral transforms to the DeWitt series for the heat kernel of the corresponding operator and thus represent a DeWitt-type series in the heat kernel coefficients with the coefficients of this expansion (which we call basis kernels) being some hypergeometric-type functions of the Synge world function. Basis kernels of a certain class of operator functions were found previously in terms of $N$-fold Mellin-Barnes integrals. In this paper we study series representations of the corresponding Mellin-Barnes integrals in both non-resonant and resonant cases and suggest a physical interpretation for the emerging series, which is related to the UV and IR properties of operator functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_22299 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multiple Mellin-Barnes integrals in Schwinger-DeWitt technique Barvinsky, A. O. Kalugin, A. E. Wachowski, W. High Energy Physics - Theory Mathematical Physics We consider off-diagonal asymptotic series for integral kernels of functions of Laplace-type operators on curved backgrounds. These expansions are obtained by applying integral transforms to the DeWitt series for the heat kernel of the corresponding operator and thus represent a DeWitt-type series in the heat kernel coefficients with the coefficients of this expansion (which we call basis kernels) being some hypergeometric-type functions of the Synge world function. Basis kernels of a certain class of operator functions were found previously in terms of $N$-fold Mellin-Barnes integrals. In this paper we study series representations of the corresponding Mellin-Barnes integrals in both non-resonant and resonant cases and suggest a physical interpretation for the emerging series, which is related to the UV and IR properties of operator functions. |
| title | Multiple Mellin-Barnes integrals in Schwinger-DeWitt technique |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2604.22299 |