Effective energy-momentum tensor of strong-field QED with unstable vacuum

TL;DR

This paper investigates how vacuum instability affects the energy-momentum tensor in strong-field QED with a constant electric field, providing explicit calculations and relating results to the Euler-Heisenberg effective action.

Contribution

It offers explicit formulas for the energy-momentum tensor considering vacuum instability and pair creation, connecting these to the Euler-Heisenberg effective action.

Findings

Explicit expressions for <0,in|T_{μν}|0,in> and <0,out|T_{μν}|0,in>

Analysis of divergences due to infinite electric field duration

Relation of EMT results to Euler-Heisenberg effective action

Abstract

We study the influence of a vacuum instability on the effective energy-momentum tensor (EMT) of QED, in the presence of a quasiconstant external electric field, by means of the relevant Green functions. In the case when the initial vacuum, |0,in>, differs essentially from the final vacuum, |0,out>, we find explicitly and compared both the vacuum average value of EMT, <0,in|T_{\mu \nu}|0,in>, and the matrix element, <0,out|T_{\mu \nu}|0,in>. In the course of the calculation we solve the problem of the special divergences connected with infinite time T of acting of the constant electric field. The EMT of pair created by an electric field from the initial vacuum is presented. The relations of the obtained expressions to the Euler-Heisenberg's effective action are established.