Revisiting semiclassical scalar QED in 1+1 dimensions

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 Ambjørn & Wolfram \cite{ambjorn_properties_1983}. Despite notable differences, our analysis confirms the mechanism, discussed by Ambjørn & 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.