  We derive the microcanonical partition function of the ideal relativistic
quantum gas with fixed intrinsic angular momentum as an expansion over fixed
multiplicities. We developed a group theoretical approach by generalizing known
projection techniques to the Poincare' group. Our calculation is carried out in
a quantum field framework and applies to particles with any spin. It extends
known results in literature in that it does not introduce any large volume
approximation and it takes particle spin fully into account. We provide
expressions of the microcanonical partition function at fixed multiplicities in
the limiting classical case of large volumes and large angular momenta and in
the grand-canonical ensemble. We also derive the microcanonical partition
function of the ideal relativistic quantum gas with fixed parity.
