Non-Perturbative One-Loop Effective Action for QED with Yukawa Couplings

TL;DR

This paper derives a non-perturbative one-loop effective action for QED extended with Yukawa couplings, incorporating scalar, pseudoscalar, and electromagnetic fields, using advanced regularization techniques and analyzing its properties.

Contribution

It provides the first full non-perturbative one-loop effective action for this extended QED model, including both even and odd parts related to chiral symmetry and anomalies.

Findings

Effective action reduces to Euler-Heisenberg or Coleman-Weinberg in certain limits.

Odd part of the action relates to the chiral anomaly.

Results are invariant under chiral transformations.

Abstract

We derive the one-loop effective action for scalar, pseudoscalar, and electromagnetic fields coupled to a Dirac fermion in an extension of QED with Yukawa couplings. Using the Schwinger proper-time formalism and zeta-function regularization, we calculate the full non-perturbative effective action to one loop in the constant background field approximation. Our result is non-perturbative in the external fields, and goes beyond existing results in the literature which treat only the first non-trivial order involving the pseudoscalar. The result has an even and odd part, which are related to the modulus and phase of the fermion functional determinant. The even contribution to the effective action involves the modulus of the effective Yukawa couplings and is invariant under global chiral transformations while the odd contribution is proportional to the angle between the scalar and pseudoscalar couplings. In different limits the effective action reduces either to the Euler-Heisenberg effective action or the Coleman-Weinberg potential. We also comment on the relationship between the odd part of the effective action and the chiral anomaly in QED.