The Hot Bang state of massless fermions

TL;DR

This paper proves the existence of a fermionic analogue of the Hot Bang state, a locally thermodynamic equilibrium state with a temperature singularity, extending previous bosonic results to massless fermions.

Contribution

It provides a rigorous proof for the existence of the Hot Bang state for massless fermions and discusses related mathematical subtleties.

Findings

Existence of fermionic Hot Bang state proven.

States exhibit properties like phase-space density satisfying a transport equation.

Discussion of mathematical subtleties in fermionic case.

Abstract

In 2002, a method has been proposed by Buchholz et al. in the context of Local Quantum Physics, to characterize states that are locally in thermodynamic equilibrium. It could be shown for the model of massless bosons that these states exhibit quite interesting properties. The mean phase-space density satisfies a transport equation, and many of these states break time reversal symmetry. Moreover, an explicit example of such a state, called the Hot Bang state, could be found, which models the future of a temperature singularity. However, although the general results carry over to the fermionic case easily, the proof of existence of an analogue of the Hot Bang state is not quite that straightforward. The proof will be given in this paper. Moreover, we will discuss some of the mathematical subtleties which arise in the fermionic case.