The microcanonical ensemble of the ideal relativistic quantum gas

• Published in: The European physical journal. C, Particles and fields Vol. 51; no. 4; pp. 899 - 912
• Main Authors: Becattini, F., Ferroni, L.
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer Nature B.V 01-08-2007
• Subjects: Bosons; Mathematical analysis; Partitions; Partitions (mathematics); Relativism; Relativistic effects; Relativistic particles
• ISSN: 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-007-0340-5

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 the 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 for calculating the microcanonical partition function that is finite at finite volume and yielding the correct thermodynamic limit. Besides an immaterial overall factor, the expression obtained turns out to be the same as in the non-relativistic multi-particle approach. This work is an introduction to the derivation of the most general expression of the microcanonical partition function fixing the maximal set of observables of the Poincaré group.