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Heat kernels and resummations: The spinor case

S. A. Franchino-Viñas1,2,3, C. García-Pérez4,5,6, F. D. Mazzitelli7,8, S. Pla9, and V. Vitagliano4,5

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Phys. Rev. D 113, 025001 – Published 5 January, 2026

DOI: https://doi.org/10.1103/yjqc-mzwb

Abstract

Among the available perturbative approaches in quantum field theory, heat kernel techniques provide a powerful and geometrically transparent framework for computing effective actions in nontrivial backgrounds. In this work, resummation patterns within the heat kernel expansion are examined as a means of systematically extracting nonperturbative information. Building upon previous results for Yukawa interactions and scalar quantum electrodynamics, we extend the analysis to spinor fields, demonstrating that a recently conjectured resummation structure continues to hold. The resulting formulation yields a compact expression that resums invariants constructed from the electromagnetic tensor and its spinorial couplings, while preserving agreement with known proper-time coefficients. Beyond its immediate computational utility, the framework offers a unified perspective on the emergence of nonperturbative effects (such as Schwinger pair creation) in relation to perturbative heat kernel data, and provides a basis for future extensions to curved spacetimes and non-Abelian gauge theories.

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Phys. Rev. D 113, 025001– Published 5 January, 2026
  • Received 5 November 2025
  • Accepted 10 December 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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