Different definitions of the chemical potential with identical partition function in QCD on a lattice

TL;DR

This paper explores different formulations of the chemical potential in lattice QCD, demonstrating that the same transfer matrix can lead to multiple actions with distinct couplings to temporal links.

Contribution

It shows that from a single transfer matrix formulation, one can derive different lattice actions with varying couplings of the chemical potential.

Findings

Multiple lattice actions with identical partition functions can be derived from a single transfer matrix.

The chemical potential can be coupled or decoupled from temporal links in different formulations.

The approach unifies different definitions of chemical potential in lattice QCD.

Abstract

It is shown that starting from one and the same transfer matrix formulation of QCD on a lattice, it is possible to obtain both the action of Hasenfratz and Karsch as well as an action where the chemical potential is not coupled to the temporal links.