Non-Perturbative One-Loop Effective Action for Electrodynamics in Curved Spacetime

TL;DR

This paper calculates the one-loop effective action for scalar and spinor fields in curved spacetime with a strong magnetic field, revealing significant gravitational effects on vacuum energy, especially for small-mass charged spinors.

Contribution

It provides an explicit non-perturbative evaluation of the one-loop effective action in curved spacetime with strong magnetic fields using zeta function regularization.

Findings

Effective action computed to all orders in magnetic field and linear in curvature.

Vacuum energy of small-mass charged spinors becomes very large due to gravitational correction.

Results applicable to massless scalar and spinor fields in curved backgrounds.

Abstract

In this paper we explicitly evaluate the one-loop effective action in four dimensions for scalar and spinor fields under the influence of a strong, covariantly constant, magnetic field in curved spacetime. In the framework of zeta function regularization, we find the one-loop effective action to all orders in the magnetic field up to linear terms in the Riemannian curvature. As a particular case, we also obtain the one-loop effective action for massless scalar and spinor fields. In this setting, we found that the vacuum energy of charged spinors with small mass becomes very large due entirely by the gravitational correction.