The relativistic Bose gas in an even-dimensional space

Abstract

The thermodynamic behaviour of a massive relativistic ideal Bose gas in an (even) d-dimensional space is studied. The thermodynamic functions are expressed as polynomials (or rational functions) in k_BT/mc² whose coefficients are proportional to the Bose-Einstein functions. Their closed forms permit a complete analytic discussion of the crossover from the non-relativistic limit to the ultra-relativistic limit. This transition is equivalent to the dimensional crossover from a d-dimensional to a 2d-dimensional nonrelativistic gas behaviour.