Reduction for one-loop tensor Feynman integrals in the relativistic quantum field theories at finite temperature and/or finite density

Abstract: 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.