Single-Particle Representations of Current Algebras

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 $\mathrm{SU}\left(6\right)\mathrm{}$ algebra the momentum must be zero, while for the chiral $\mathrm{SU}\left(3\right)\mathrm{}\otimes \mathrm{SU}\left(3\right)\mathrm{}$ algebra it must be infinite. In this single-particle limit it is shown that the chiral algebra is equivalent to the collinear $\mathrm{SU}\left(3\right)\mathrm{}\otimes \mathrm{SU}\left(3\right)\mathrm{}$ subalgebra of $\mathrm{SU}\left(6\right)\mathrm{}$, and so a relation between the $\mathrm{SU}\left(6\right)\mathrm{}$ and chiral algebras is established.