The European Physical Journal C

, Volume 51, Issue 4, pp 899–912 | Cite as

The microcanonical ensemble of the ideal relativistic quantum gas

  • F. BecattiniEmail author
  • L. Ferroni
Regular Article - Theoretical Physics


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.


Thermodynamic Limit Region Versus Particle Multiplicity Microcanonical Ensemble Compton Wavelength 
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Copyright information

© Springer-Verlag / Società Italiana di Fisica 2007

Authors and Affiliations

  1. 1.Università di Firenze and INFN Sezione di FirenzeFirenzeItaly

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