A path integration approach to relativistic finite density problems and its particle content

TL;DR

This paper develops a path integration approach for relativistic finite density problems, demonstrating consistency with thermodynamics and introducing a novel fermion representation with potential observable effects.

Contribution

It introduces a new 8-component real representation for fermion fields in finite density quantum field theory, differing from the conventional 4-component approach.

Findings

Path integration formulation aligns with thermodynamics at finite density.

New fermion representation exhibits a mirror universe with observable effects.

Approach smoothly connects to relativistic quantum field theory at zero temperature.

Abstract

A path integration formulation for the finite density and temperature problems is shown to be consistent with the thermodynamics using an 8 component ``real'' representation for the fermion fields by applying it to a free fermion system. A relativistic quantum field theory is shown to be smoothly approached at zero temperature by a real-time thermal field theory so derived even at a finite density. The analysis leads to a new representation for the fermion fields which is shown to be inequivalent to the conventional 4 component theory at the quantum level by having a mirror universe with observable effects and to be better behaved at short distances.