Algebra of Spin Currents and the Relativistic Formulation ofSU(6)

Abstract

The infinite algebra of covariant spin current densities is studied. It is generated by local second-rank tensor operators odd under charge conjugation $C$, and involves tensors of higher rank that can be $C$ even or $C$ odd. Explicit constructions are given for $S=\frac{1}{2}, 0, \mathrm{and} 1$. The spin algebra is assumed to be valid for fields with nonderivative interaction. The algebra is generalized when an internal symmetry group like $\mathrm{SU}(3)$ is present. It is then shown that on one-particle states the algebra closes, giving an $\mathrm{SU}(6)\ensuremath{\bigotimes}\mathrm{SU}(6)$ symmetry group, magnetic-moment operators being among the generators. When two-particle states are considered, the algebra involves $C$-even longitudinal (with respect to the relative momentum) and $C$-odd transverse spin operators that close, giving an $S{U}_{W}(6)$ algebra which remains valid when we restrict ourselves to the matrix elements of the spin algebra between two one-particle states. Saturation of this algebra by the (56,1) representation of the one-particle symmetry group gives nonzero anomalous magnetic moments and the same ratio $\frac{D}{F}=\ensuremath{-}\frac{{\ensuremath{\mu}}_{p}}{{\ensuremath{\mu}}_{n}}=\frac{3}{2}$ as in the nonrelativistic $\mathrm{SU}(6)$ group.