QED Effective Actions in Inhomogeneous Backgrounds: Summing the Derivative Expansion

TL;DR

This paper investigates the effectiveness of the derivative expansion method for calculating QED effective actions in inhomogeneous electromagnetic backgrounds, using exactly solvable models to test convergence and improve understanding of pair-production phenomena.

Contribution

The study provides precision tests of the derivative expansion in inhomogeneous backgrounds, revealing its convergence properties and deriving exponential corrections to Schwinger's pair-production formula.

Findings

The derivative expansion converges/diverges depending on background inhomogeneity.

Exact solutions enable precise testing of approximation methods.

Exponential corrections to pair-production are derived for inhomogeneous fields.

Abstract

The QED effective action encodes nonlinear interactions due to quantum vacuum polarization effects. While much is known for the special case of electrons in a constant electromagnetic field (the Euler-Heisenberg case), much less is known for inhomogeneous backgrounds. Such backgrounds are more relevant to experimental situations. One way to treat inhomogeneous backgrounds is the "derivative expansion", in which one formally expands around the soluble constant-field case. In this talk I use some recent exactly soluble inhomogeneous backgrounds to perform precision tests on the derivative expansion, to learn in what sense it converges or diverges. A closely related question is to find the exponential correction to Schwinger's pair-production formula for a constant electric field, when the electric background is inhomogeneous.