Backreaction and Particle Production in (3+1)-dimensional QED

TL;DR

This paper investigates fermion pair production in a strong electric field within (3+1)-dimensional QED, analyzing the dynamics of the resulting plasma and its energy-momentum evolution using boost-invariant coordinates.

Contribution

It derives and solves renormalized equations for the electric field and particle current in (3+1) dimensions, extending previous (1+1)-dimensional models to more realistic scenarios.

Findings

Energy density closely follows longitudinal pressure, unlike in lower dimensions.

Transverse momentum distribution at large momentum is significantly larger than constant field predictions.

The model provides detailed proper-time evolution of plasma properties in heavy-ion collision analogs.

Abstract

We study the fermion pair production from a strong electric field in boost-invariant coordinates in (3+1) dimensions and exploit the cylindrical symmetry of the problem. This problem has been used previously as a toy model for populating the central-rapidity region of a heavy-ion collision (when we can replace the electric by a chromoelectric field). We derive and solve the renormalized equations for the dynamics of the mean electric field and current of the produced particles, when the field is taken to be a function only of the fluid proper time $\tau = \sqrt{t^2-z^2}$. We determine the proper-time evolution of the comoving energy density and pressure of the ensuing plasma and the time evolution of suitable interpolating number operators. We find that unlike in (1+1) dimensions, the energy density closely follows the longitudinal pressure. The transverse momentum distribution of fermion pairs at large momentum is quite different and larger than that expected from the constant field result.