Particle number in kinetic theory

TL;DR

This paper derives expressions for particle number densities in phase space for scalar and fermionic fields using Wigner functions, ensuring physical consistency and applying them to cosmological scenarios.

Contribution

It introduces a unified derivation of particle number densities for both bosons and fermions in phase space, consistent with thermal field theory and applicable to cosmological models.

Findings

Particle number for bosons is positive.

Fermion particle number ranges between zero and one.

Expressions are consistent with thermal field theory.

Abstract

We provide a derivation for the particle number densities on phase space for scalar and fermionic fields in terms of Wigner functions. Our expressions satisfy the desired properties: for bosons the particle number is positive, for fermions it lies in the interval between zero and one, and both are consistent with thermal field theory. As applications we consider the Bunch-Davies vacuum and fermionic preheating after inflation.