Currents, chemical potential and boundary conditions in lattice QCD

TL;DR

This paper explores the relationship between fermionic currents and boundary conditions in lattice QCD, deriving the action with chemical potential and connecting Fock space to boundary conditions.

Contribution

It establishes a link between operator and Grassmannian currents, derives the QCD action with chemical potential, and discusses boundary conditions in lattice formulations.

Findings

Derived the QCD action with non-zero chemical potential.

Connected fermionic Fock space to boundary conditions.

Analyzed the relation between operator and Grassmannian currents.

Abstract

A connection between the operator fermionic currents $\hatJ$ and corresponding `Grassmannian' currents $J$ in the functional integral formalism is studied. The QCD action with non--zero chemical potential $\mu$ is derived. A connection between the fermionic Fock space and boundary conditions along the forth direction is discussed.