  The \emph{conventional} Passarino-Veltman reduction is a systematic procedure
based on the Lorentz covariance, which can efficiently reduce the one-loop
tensor Feynman integrals in the relativistic quantum field theories (QFTs) at
zero temperature and zero density. However, the Lorentz covariance is
explicitly broken when either of the temperature and density is finite, due to
a rest reference frame of the many-body system in which the temperature and
density are measured, rendering the \emph{conventional} Passarino-Veltman
reduction not applicable anymore to reduce the one-loop tensor Feynman
integrals therein. In this paper, we report a \emph{generalized}
Passarino-Veltman reduction which can efficiently simplify the one-loop tensor
Feynman integrals in the relativistic QFTs at finite temperature and/or finite
density. The \emph{generalized} Passarino-Veltman reduction can analyze the
one-loop tensor Feynman integrals in a wide range of physical systems described
by the relativistic QFTs at finite temperature and/or finite density, such as
quark-gluon plasma in nuclear physics.
