Thermal operator representation of finite-temperature amplitudes in the presence of a chemical potential

In a recent paper [Phys. Rev. D 72, 085006 (2005)], Brandt et al. deduced the thermal operator representation for a thermal N-point amplitude, both in the imaginary-time and real-time formalisms. In the case when a chemical potential present, however, the representation is not as simple as in the case with vanishing chemical potential. We propose a much simpler and transparent representation for the case of nonzero chemical potential.