Applications of Mellin transforms to the statistical mechanics of ideal quantum gases

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Abstract
It is well known that the Boltzmann partition function for noninteracting particles factors into a product of N single-particle partition functions. We show here that, in much the same way, the logarithm of the grand partition function of quantum statistical mechanics for ideal gases is represented by a contour integral containing the single-particle partition function. The unification achieved in this way is illustrated by applications to field-free nonrelativistic particles, collections of relativistic particles, systems in the presence of a uniform mangetic field, and inhomogeneous systems in equilibrium. Both Fermi and Bose statistics are encompassed in the treatment.

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