Heat Kernels and Resummations: the Spinor Case

TL;DR

This paper extends heat kernel resummation techniques to spinor fields in quantum field theory, providing a compact nonperturbative formulation that aligns with known coefficients and offers insights into phenomena like Schwinger pair creation.

Contribution

It demonstrates that a conjectured resummation structure applies to spinor fields, unifying perturbative and nonperturbative aspects in heat kernel expansions.

Findings

Resummation pattern holds for spinor fields.

Derived compact expression for nonperturbative invariants.

Framework relates nonperturbative effects to perturbative data.

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.