Gravitational corrections to the Euler-Heisenberg Lagrangian

TL;DR

This paper derives a generalized Euler-Heisenberg Lagrangian incorporating gravitational corrections using the worldline formalism, providing a new framework for understanding quantum effects in combined electromagnetic and gravitational fields.

Contribution

It introduces a novel method to compute the one-loop effective action with gravitational corrections, extending the Euler-Heisenberg Lagrangian to Einstein-Maxwell backgrounds.

Findings

Derived a generalized effective action including gravitational effects.

Compared results with previous approaches and discussed applications.

Provided a framework for future studies of quantum fields in curved spacetime.

Abstract

We use the worldline formalism for calculating the one-loop effective action for the Einstein-Maxwell background induced by charged scalars or spinors, in the limit of low energy and weak gravitational field but treating the electromagnetic field nonperturbatively. The effective action is obtained in a form which generalizes the standard proper-time representation of the Euler-Heisenberg Lagrangian. We compare with previous work and discuss possible applications.