Gauge-Invariant Quantities Characterizing Gauge Fields in Chromodynamics

TL;DR

This paper computes Lorentz- and gauge-invariant quantities related to gauge fields in SU(3) and SU(2) chromodynamics, providing tools for better understanding gauge field characteristics.

Contribution

It introduces explicit calculations of gauge-invariant quantities involving the product of generators and field strength tensors in SU(3) and SU(2).

Findings

Derived Lorentz-invariant, gauge-invariant quantities for SU(3) and SU(2).

Provided formulas for the product of generators and field strengths.

Enhanced understanding of gauge field properties in QCD.

Abstract

We calculate Lorentz-invariant and gauge-invariant quantities characterizing the product $\sum_a D_R(T^a) F^a_{\mu\nu}$, 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.