# Particle Production in Strong Time-dependent Fields

## TL;DR

This paper introduces a kinetic equation approach to analyze particle-antiparticle pair production in strong, time-varying external fields, emphasizing the dynamics and phase transition characteristics of the process.

## Contribution

It derives the kinetic equations for fermions and bosons from fundamental equations and applies them to various external field pulse configurations, highlighting system evolution and phase transition features.

## Key findings

- Time evolution shows characteristics of a field-induced phase transition.
- Entropy and particle density behaviors indicate system dynamics during pair production.
- Application to laser field pulses demonstrates the approach's versatility.

## Abstract

In these lecture notes we give an introduction to the kinetic equation approach to pair production form the vacuum in strong, time-dependent external fields (dynamical Schwinger process). We first give a derivation of the kinetic equation with the source term for the case of fermions starting from the Dirac equation and for bosons from the Klein-Gordon equation. In a second part we discuss the application of the approach to the situation of external field pulses as single-sheeted functions of time (like the Sauter-pulse) and as multi- sheeted functions approximating the situation in the focal point of counter-propagating laser beams. Special emphasis is on the discussion of the time evolution of the system that exhibits the characteristics of a field-induced phase transition for which we discuss the behaviour of the entropy and particle density of the system. We give an outlook to applications of the approach in describing particle production in strong fields formed in particle and nuclear collisions.