Effective Action of QED in Electric Field Backgrounds

TL;DR

This paper derives the exact one-loop effective action for scalar and spinor QED in specific electric fields, linking vacuum persistence to pair creation, using the evolution operator method and Bogoliubov coefficients.

Contribution

It provides an exact calculation of the effective action for Sauter-type electric fields, demonstrating the relation between vacuum persistence and pair creation.

Findings

Exact effective action for Sauter-type electric field obtained

Vacuum persistence correctly related to pair creation rate

Renormalized effective action confirms theoretical relations

Abstract

We use the evolution operator method to find the one-loop effective action of scalar and spinor QED in electric field backgrounds in terms of the Bogoliubov coefficient between the ingoing and the outgoing vacua. We obtain the exact one-loop effective action for a Sauter-type electric field, E_0 sech^2 (t/tau), and show that the imaginary part correctly yields the vacuum persistence. The renormalized effective action shows the general relation between the vacuum persistence and the total mean number of created pairs for the constant and the Sauter-type electric field.