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

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.