  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.
