Statistical properties of states in QED with unstable vacuum

TL;DR

This paper analyzes the statistical properties and entropy of quantum states in QED with unstable vacuum, using a nonperturbative approach and explicit calculations in a T-constant electric field background.

Contribution

It provides a nonperturbative framework for studying the statistical properties of charged quantum fields in unstable vacua, including explicit calculations in a solvable electric field model.

Findings

Entropy increases due to partial state reductions.

Decoherence effects are analyzed in the evolution of QED states.

Explicit statistical properties are derived for a specific electric field background.

Abstract

We study statistical properties of states of massive quantized charged Dirac and Klein-Gordon fields interacting with a background that violates the vacuum stability, first in general terms and then for a special electromagnetic background. As a starting point, we use a nonperturbative expression for the density operators of such fields derived by Gavrilov et al [S.P. Gavrilov, D.M. Gitman, and J.L. Tomazelli, Nucl. Phys. B 795, 645 (2008)]. We construct the reduced density operators for electron and positron subsystems and discuss a decoherence that may occur in the course of the evolution due to an intermediate measurement. By calculating the entropy we study the loss of the information in QED states due to partial reductions and a possible decoherence. Next, we consider the so-called T-constant external electric field as an external background. This exactly solvable example allows us to calculate explicitly all statistical properties of various quantum states of the massive charged fields under consideration.