The chemical potential in the transfer matrix and in the path integral formulation of QCD on a lattice

TL;DR

This paper explores how the chemical potential is incorporated into the transfer matrix and path integral formulations of lattice QCD, deriving the Hasenfratz-Karsh action for different fermion types and discussing basis-related issues.

Contribution

It introduces a formal definition of chemical potential as a Lagrange multiplier in the transfer matrix approach and derives the corresponding Euclidean path integral form for Wilson and Kogut-Susskind fermions.

Findings

Derived the Hasenfratz-Karsh action for Wilson fermions.

Established the relation of chemical potential in different fermion bases.

Identified open problems in the spin-diagonal basis.

Abstract

We define the chemical potential as the Lagrange multiplier of the baryon charge operator in the transfer matrix formalism of QCD on a lattice. Transforming the partition function into an euclidean path integral we get the Hasenfratz-Karsh action both for Wilson and Kogut-Susskind fermions. In the latter case the chemical potential in the spin-diagonal basis is half that in the flavour basis. Some open problems in the spin-diagonal basis are pointed out.