Fermion pair production in QED and the backreaction problem in (1+1)-dimensional boost-invariant coordinates revisited

TL;DR

This paper investigates fermion pair production in (1+1)-dimensional QED with backreaction, comparing two initial conditions for fermions and analyzing their effects on the evolution of electric fields and related quantities.

Contribution

It introduces and compares two initial conditions for fermions in pair production with backreaction, demonstrating their similar physical outcomes and computational efficiency.

Findings

Both initial conditions yield similar physical results.

The 'free field' initial condition is computationally more efficient.

Proper time evolution of electric field and current is characterized.

Abstract

We study two different initial conditions for fermions for the problem of pair production of fermions coupled to a classical electromagnetic field with backreaction in \oneplusone boost-invariant coordinates. Both of these conditions are consistent with fermions initially in a vacuum state. We present results for the proper time evolution of the electric field $E$, the current, the matter energy density, and the pressure as a function of the proper time for these two cases. We also determine the interpolating number density as a function of the proper time. We find that when we use a "first order adiabatic" vacuum initial condition or a "free field" initial condition for the fermion field, we obtain essentially similar behavior for physically measurable quantities. The second method is computationally simpler, it is twice as fast and involves half the storage required by the first method.