QUANTUM PHASE-SPACE FOR AN IDEAL RELATIVISTIC GAS IN D-SPATIAL DIMENSIONS

We present the closed formula for the d-dimensional invariant phase-space integral for an ideal relativistic gas in an exact integral form. In the particular cases of the nonrelativistic and the extreme relativistic limits the phase-space integrals are calculated analytically. Then we consider the d-dimensional invariant phase space with quantum statistics and derive the cluster decomposition for the grand canonical and canonical partition functions as well as for the microcanonical and grand microcanonical densities of states. As a showcase, we consider the black-body radiation in d dimensions.