SU($N$) Cartan-Weyl bases and color factors

Abstract

Constant temporal backgrounds have become a convenient tool for the discussion of continuum non-abelian gauge theories at finite temperature, as they provide a grasp on the confinement/deconfinement transition. It has been pointed that such backgrounds are better dealt with within so-called Cartan-Weyl color bases, rather than within the standard Cartesian bases. Here, we discuss the specificities of the evaluation of SU($N$) color factors within these bases, extending the discussion in Ref. [1].