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

TL;DR

This paper introduces a generalized Passarino-Veltman reduction method that efficiently simplifies one-loop tensor Feynman integrals in relativistic quantum field theories at finite temperature and density, where the conventional method fails due to broken Lorentz covariance.

Contribution

The paper develops a new generalized reduction technique applicable to finite temperature and density QFTs, extending the conventional Lorentz-covariance-based method.

Findings

Effective reduction of tensor integrals at finite temperature/density.

Applicable to systems like quark-gluon plasma.

Overcomes limitations of conventional methods.

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.