  We derive the microcanonical partition function of the ideal relativistic
quantum gas of spinless bosons in a quantum field framework as an expansion
over fixed multiplicities. Our calculation generalizes well known expressions
in literature in that it does not introduce any large volume approximation and
it is valid at any volume. We discuss the issues concerned with the definition
of the microcanonical ensemble for a free quantum field at volumes comparable
with the Compton wavelength and provide a consistent prescription of
calculating the microcanonical partition function, which is finite at finite
volume and yielding the correct thermodynamic limit. Besides an immaterial
overall factor, the obtained expression turns out to be the same as in the
non-relativistic multi-particle approach. This work is introductory to derive
the most general expression of the microcanonical partition function fixing the
maximal set of observables of the Poincare' group.
