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Register a new userThe microcanonical ensemble of the ideal relativistic quantum gas
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Added by
Francesco Becattini
Publication date
2007
fields
Physics
and research's language is
English
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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.
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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.
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