Unitarity and vacuum deformation in QED with critical potential steps

TL;DR

This paper investigates how critical potential steps in QED affect vacuum states, unitarity, and entanglement, extending previous nonperturbative work and analyzing vacuum deformation and information loss.

Contribution

It develops a framework for describing vacuum deformation in QED with critical potential steps and analyzes the resulting entanglement and unitarity properties.

Findings

Vacuum deformation depends on the critical potential steps.

Loss of information occurs in electron and positron subsystems.

Entanglement measures increase with potential step strength.

Abstract

The present article can be considered as a complement to the work P.R.D 93, 045002 (2016) where an nonperturbative approach to QED with x-electric critical potential steps was developed. In the beginning we study conditions when in- and out-spaces of the QED under consideration are unitarily equivalent. Then we construct a general density operator with the vacuum initial condition. Such an operator describes a deformation of the initial vacuum state by x-electric critical potential steps. We construct reductions of the deformed state to electron and positron subsystems, calculating the loss of the information in these reductions. We illustrate the general consideration studying the deformation of the quantum vacuum between two capacitor plates. Finally we calculate the entanglement measures of these reduced matrices as von Neumann entropies.