Heat Kernels and Resummations: the Spinor Case

TL;DR

The paper extends heat-kernel resummation techniques to spinor fields in electromagnetic backgrounds, producing a closed-form, nonperturbative resummation that captures all contracted invariants of the field strength in the coincidence limit while remaining consistent with known Seeley–DeWitt coefficients. The authors prove that, in this spinor case and in arbitrary even dimensions, the essential field-strength information is encoded in a background-dependent prefactor, with the remaining contributions organized into a background-free series in the coincidence limit. This framework unifies perturbative data with nonperturbative phenomena such as Schwinger pair creation and provides a foundation for generalisations to curved spacetimes and non-Abelian backgrounds, with potential phenomenological applications in strong-field and cosmological settings.

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.