Spacetime-dependent electric field effects in vacuum and plasma using the Wigner-formalism

TL;DR

This paper develops a Wigner-formalism-based framework to analyze how strong, spacetime-dependent electric fields influence vacuum and plasma phenomena, including wave propagation and Schwinger pair production.

Contribution

It derives a new set of coupled PDEs for the Wigner function in arbitrary strong electromagnetic fields and applies them to plasma wave propagation and pair production scenarios.

Findings

Dispersion relation for plasma waves in strong fields derived.

Dependence of pair production rate on perpendicular momentum analyzed.

Electric field strength influences the spread of produced pairs.

Abstract

We derive a system of coupled partial differential equations for the equal-time Wigner function in an arbitrary strong electromagnetic field using the Dirac-Heisenberg-Wigner formalism. In the electrostatic limit, we present a 3+1-system of four coupled partial differential equations, which are completed by Ampere's law. This electrostatic system is further studied for two different cases. In the first case, we consider linearized wave propagation in plasma accounting for the nonzero vacuum expectation values. We then derive the dispersion relation and compare it with well-known limiting cases. In the second case, we consider Schwinger pair production using the local density approximation to allow for analytical treatment. The dependence of the pair production rate on the perpendicular momentum is investigated and it turns out that the spread of the produced pairs along with perpendicular momentum depends on the strength of the applied electric field.