Revisiting semiclassical scalar QED in 1+1 dimensions

TL;DR

This paper investigates the effects of backreaction in a 1+1 dimensional scalar QED system with boundary charges, correcting previous work and revealing phenomena like over-screening.

Contribution

It revisits and extends prior analyses of boundary effects in scalar QED, clarifying backreaction mechanisms and introducing the concept of over-screening in this context.

Findings

Backreaction avoids certain instabilities in the system.

Confirmation of the mechanism by which backreaction stabilizes the system.

Discovery of over-screening where increased external charges reduce the electric field.

Abstract

We study the backreaction of a charged scalar quantum field in the presence of two opposite charges placed at the boundaries of a finite one-dimensional region, with attention to boundary effects. We review, correct, and extend previous corresponding work of Ambj{\o}rn \& Wolfram \cite{ambjorn_properties_1983}. Despite notable differences, our analysis confirms the mechanism, discussed by Ambj{\o}rn \& Wolfram, by which the incorporation of backreaction avoids certain instabilities. We also observe the interesting phenomenon of ``over-screening'', by which for high external charges an increase of the external charges leads to a decrease of the electric field between the two charges.