Single-Particle Representations of Current Algebras

Abstract

The requirement that matrix elements of current commutators are saturated by single-particle intermediate states leads to kinematical restrictions on the allowed momenta of these states. For the $\mathrm{SU}(6)$ algebra the momentum must be zero, while for the chiral $\mathrm{SU}(3)\ensuremath{\bigotimes}\mathrm{SU}(3)$ algebra it must be infinite. In this single-particle limit it is shown that the chiral algebra is equivalent to the collinear $\mathrm{SU}(3)\ensuremath{\bigotimes}\mathrm{SU}(3)$ subalgebra of $\mathrm{SU}(6)$, and so a relation between the $\mathrm{SU}(6)$ and chiral algebras is established.