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Multiple Mellin-Barnes integrals in Schwinger-DeWitt technique

A. O. Barvinsky1,2,*, A. E. Kalugin1,†, and W. Wachowski1,‡

  • *Contact author: barvin@td.lpi.ru
  • †Contact author: kalugin.ae@phystech.edu
  • ‡Contact author: vladvakh@gmail.com
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Phys. Rev. D 114, 105013 – Published 10 November, 2026

DOI: https://doi.org/10.1103/bsyy-tk74

Abstract

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 and some hypergeometric-type functions of the Synge world function (which we call basis kernels). Basis kernels of 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 nonresonant and resonant cases and suggest a physical interpretation for the emerging series, which is related to the UV and IR properties of operator functions.

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Phys. Rev. D 114, 105013– Published 10 November, 2026
  • Received 7 July 2026
  • Accepted 20 October 2026
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