In this paper, we formulate a q-deformed many-body theory for the relativistic Fermi gas and discuss the effects of the deformation parameter q on physical properties of such systems. Since antiparticle excitations appear in the relativistic regime, a suitable treatment to the choice of deformation parameters for both fermions and antifermions must be carefully taken in order to get a consistent theory. By applying this formulation, we further study the thermostatistic properties of a q-deformed ideal relativistic Fermi gas. It can be shown that even in the noninteracting scenario, the system exhibits interesting characteristics which are significantly different from ordinary Fermi gases. Explicitly, antiparticles may become dominant due to the shift of chemical potential by the deformation parameter q. This may build a solid foundation for the further studies of q-deformed relativistic interacting systems.

中文翻译：

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aq-变形的相对论理想费米气体的热力学

在本文中，我们为相对论费米气体制定了 q 变形多体理论，并讨论了变形参数 q 对此类系统物理性质的影响。由于反粒子激发出现在相对论体系中，因此必须谨慎地对费米子和反费米子的变形参数选择进行适当的处​​理，以获得一致的理论。通过应用该公式，我们进一步研究了 q 变形的理想相对论费米气体的恒温特性。可以证明，即使在非相互作用的情况下，该系统也表现出与普通费米气体显着不同的有趣特征。明确地，由于变形参数 q 引起的化学势移动，反粒子可能成为主导。