In-Out Formalism for One-Loop Effective Actions in QED and Gravity

TL;DR

This paper discusses the in-out formalism for calculating one-loop effective actions in QED and gravity, illustrating its application in electromagnetic and curved spacetime backgrounds, highlighting the connection between vacuum polarization and pair production.

Contribution

It introduces a systematic approach to compute effective actions in known field solutions, emphasizing the relation between real and imaginary parts in pair production scenarios.

Findings

Effective action in constant electric fields in Minkowski space.

Effective action in uniform electric fields in (A)dS space.

Conjecture of one-to-one correspondence between vacuum polarization and pair production.

Abstract

The in-out formalism is a systematic and powerful method for finding the effective actions in an electromagnetic field and a curved spacetime provided that the field equation has explicitly known solutions. The effective action becomes complex when pairs of charged particles are produced due to an electric field and curved spacetime. This may lead to a conjecture of one-to-one correspondence between the vacuum polarization (real part) and the vacuum persistence (imaginary part). We illustrate the one-loop effective action in a constant electric field in a Minkowski spacetime and in a uniform electric field in a two-dimensional (anti-) de sitter space.