QCD in the Color-Flow Representation

TL;DR

This paper introduces a new derivation of SU(N) QCD interactions in the color-flow basis by extending the gauge group, providing a framework that simplifies calculations and extends to exotic representations, with implications for computational tools.

Contribution

It presents a novel derivation of SU(N) interactions in the color-flow basis via an extended gauge group, including new Feynman rules for exotic representations and practical computational applications.

Findings

Extended gauge group to U(N)×U(1)' with canceling factors

Derived equivalence to standard basis to all orders

Extended Feynman rules for exotic color representations

Abstract

For many practical purposes, it is convenient to formulate unbroken non-abelian gauge theories like QCD in a color-flow basis. We present a new derivation of SU(N) interactions in the color-flow basis by extending the gauge group to U(N)xU(1)' in such a way that the two U(1) factors cancel each other. We use the quantum action principles to show the equivalence to the usual basis to all orders in perturbation theory. We extend the known Feynman rules to exotic color representations (e.g. sextets) and interactions (e.g. $\epsilon_{ijk}$). We discuss practical applications as they occur in automatic computation programs.