Fermionic and bosonic pair creation in an external electric field at finite temperature using the functional Schr\"odinger representation

TL;DR

This paper analyzes how fermions and bosons are created in an external electric field at finite temperature, using the functional Schrödinger representation to compute particle production, distributions, and probabilities over time.

Contribution

It extends the functional Schrödinger representation to include fermionic fields and incorporates finite temperature effects in the analysis of particle creation.

Findings

Particle production depends on the external electric field and temperature.

The distribution of created particles in momentum space is characterized.

Thermal contributions significantly affect particle creation probabilities.

Abstract

We solve the time evolution of the density matrix both for fermions and bosons in the presence of a homogeneous but time dependent external electric field. The number of particles produced by the external field, as well as their distribution in momentum space is found for finite times. Furthermore, we calculate the probability of finding a given number of particles in the ensemble. In all cases, there is a nonvanishing thermal contribution. The bosonic and the fermionic density matrices are expressed in a "functional field basis". This constitutes an extension of the "field basis" concept to fermions.