理想相对论量子气体的微正则系综
The microcanonical ensemble of the ideal relativistic quantum gas
摘要：
在量子场框架下，我们导出了理想相对论性无自旋玻色子量子气体的微正则配分函数。我们的计算推广了文献中众所周知的表达式，因为它没有引入任何大体积近似，并且在任何体积下都是有效的。讨论了在体积与康普顿波长相当的自由量子场中微正则系综的定义问题，并给出了计算微正则配分函数的一致性公式，该公式在有限体积下是有限的，并给出了正确的热力学极限。除了一个非物质的整体因素，得到的表达式原来是相同的非相对论多粒子方法。本文导出了确定庞加莱群最大观测量集的微正则配分函数的最一般表达式。
英文摘要：
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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