Gauge-Invariant Quantities Characterizing Gauge Fields in Chromodynamics

Abstract

We calculate Lorentz-invariant and gauge-invariant quantities characterizing the product ${\sum }_a{D}_R(T^a)F_{\mu \nu }^a$, where $D_R(T^a)$ denotes the matrix for the generator $T^a$ in the representation $R=$ fundamental and adjoint, for color SU(3). We also present analogous results for an SU(2) gauge theory.