Derivative corrections to the Heisenberg-Euler effective action

TL;DR

This paper derives the leading derivative corrections to the Heisenberg-Euler effective action using vacuum polarization tensor evaluations, providing explicit formulas and applications to pair production in slowly-varying fields.

Contribution

It introduces an efficient method to compute derivative corrections to the Heisenberg-Euler action from the vacuum polarization tensor, including explicit integral representations and closed-form results.

Findings

Explicit parameter-integral representation for derivative corrections

Closed-form results for magnetic and electric field configurations

Leading correction to Schwinger's pair production formula

Abstract

We show that the leading derivative corrections to the Heisenberg-Euler effective action can be determined efficiently from the vacuum polarization tensor evaluated in a homogeneous constant background field. After deriving the explicit parameter-integral representation for the leading derivative corrections in generic electromagnetic fields at one loop, we specialize to the cases of magnetic- and electric-like field configurations characterized by the vanishing of one of the secular invariants of the electromagnetic field. In these cases, closed-form results and the associated all-orders weak- and strong-field expansions can be worked out. One immediate application is the leading derivative correction to the renowned Schwinger-formula describing the decay of the quantum vacuum via electron-positron pair production in slowly-varying electric fields.