A dimensionally reduced expression for the QCD fermion determinant at finite temperature and chemical potential

TL;DR

This paper derives a simplified, dimensionally reduced formula for the QCD fermion determinant at finite temperature and chemical potential, enhancing understanding of its dependence on these parameters and aiding phase transition analysis.

Contribution

It introduces a novel dimensionally reduced expression for the QCD fermion determinant applicable to general gauge fields, extending previous free fermion results.

Findings

Expression reduces to a simple form at low temperature

Provides a rigorous derivation in continuous time--lattice space

Outlines a method to study QCD phase transitions at zero temperature and nonzero density

Abstract

A dimensionally reduced expression for the QCD fermion determinant at finite temperature and chemical potential is derived which sheds light on the determinant's dependence on these quantities. This is done via a partial zeta regularisation, formally applying a general formula for the zeta-determinant of a differential operator in one variable with operator-valued coefficients. The resulting expression generalises the known one for the free fermion determinant, obtained via Matsubara frequency summation, to the case of general background gauge field; moreover there is no undetermined overall factor. Rigorous versions of this result are obtained in a continuous time--lattice space setting. The determinant expression reduces to a remarkably simple form in the low temperature limit. A program for how to use this to obtain insight into the QCD phase transition at zero temperature and nonzero density is outlined.