Finite Temperature Path Integral Method for Fermions and Bosons

The calculation of the density matrix for fermions and bosons in the Grand Canonical Ensemble allows an efficient way for the inclusion of fermionic and bosonic statistics at all temperatures. It was shown that in a Path Integral Formulation fermionic density matrix can be expressed via an integration over a novel representation of the universal temperature dependent functional. While several representations for the universal functional have already been developed, they are usually presented in a form inconvenient for computer calculations. In this brief report we discuss a new representation for the universal functional in terms of the Hankel functions which is advantageous for computational applications.