Quark color algebra in Adler's chromostatics

Abstract

I study quark color charge algebras and investigate general outer products which satisfy the Jacobi identity and inner products which are consistent with the trace condition. The two-quark case is treated in detail. For three or more quarks, only two kinds of outer products are possible, neither of which satisfies the restricted trace condition in the simplest formulation of the color charge algebra. A three-copy theory is constructed so that the restricted trace condition is satisfied in the three-quark case.