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Regularization of functional determinants of radial operators via heat kernel coefficients

Yutaro Shoji1 and Masahide Yamaguchi2,3,4

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Phys. Rev. D 112, 125002 – Published 1 December, 2025

DOI: https://doi.org/10.1103/k1b6-2gbs

Abstract

We propose an efficient regularization method for functional determinants of radial operators using heat kernel coefficients. Our key finding is a systematic way to identify heat kernel coefficients in the angular momentum space. We explicitly obtain the formulas up to sixth order in the heat kernel expansion, which suffice to regularize up to 13-dimensional functional determinants. We find that the heat kernel coefficients accurately approximate the large angular momentum dependence of functional determinants, and make numerical computations more efficient. In the limit of a large angular momentum, our formulas reduce to the Wentzel-Kramers-Brillouin formulas in previous studies, but are extended to higher orders. All the results are available in both the zeta function regularization and the dimensional regularization.

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Phys. Rev. D 112, 125002– Published 1 December, 2025
  • Received 29 September 2025
  • Accepted 9 November 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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