Dynamical derivation of a quantum kinetic equation for particle production in the Schwinger mechanism

TL;DR

This paper derives a non-Markovian quantum kinetic equation for particle pair production in a time-dependent electric field, incorporating the Schwinger mechanism, and compares it with existing approaches.

Contribution

It presents a new closed-form kinetic equation for pair production that includes the Schwinger source term and discusses its relation to other models.

Findings

Derived a non-Markovian kinetic equation for pair production.

Reduced the source term to the Schwinger formula in the low density limit.

Compared the new formula with other theoretical approaches.

Abstract

A quantum kinetic equation has been derived for the description of pair production in a time-dependent homogeneous electric field $E(t)$. As a source term, the Schwinger mechanism for particle creation is incorporated. Possible particle production due to collisions and collisional damping are neglected. The main result is a closed kinetic equation of the non-Markovian type. In the low density approximation, the source term is reduced to the leading part of the well known Schwinger formula for the probability of pair creation. We compare the formula obtained with other approaches and discuss the differences.