Color-charge algebras in Adler's chromodynamics

Abstract

We show that the color-charge algebra in the three-quark sector generated by the matrices of the fundamental representation of $\mathrm{U}\mathrm{}\left(n\right)\mathrm{}$ does not have the trace properties required in Adler's extension of chromodynamics. We also discuss a diagrammatic representation of algebras generated by quark and antiquark charges in general, and an embedding of the $N$-quark algebra in the symmetric group ${\mathcal{S}}_{N+1\mathrm{}}$.