Lattice fermions at non-zero temperature and chemical potential

We study the free fermion gas at finite temperature and chemical potential in the lattice regularized version proposed by Hasenfratz and Karsch and by Kogut et al. Special emphasis is placed on the identification of the particle and antiparticle contributions to the partition function. In the case of naive fermions we show that the partition function no longer separates into particle-antiparticle contributions in the way familiar from the continuum formulation. The use of Wilson fermions, on the other hand, eliminates this unpleasant feature, and leads, after subtracting the vacuum contributions, to the familiar expressions for the average energy and charge densities.