SU(3)Symmetry and Algebraic Realizations of Chiral Symmetry

Abstract

The algebraic realizations of chiral symmetry obtained by Weinberg are investigated for the case of $\mathrm{SU}\left(3\right)\mathrm{}$ symmetry. When only $p$-wave interactions are taken into account, the algebraic realization of the first superconvergence condition is given by the Lie algebra of the group $\mathrm{SU}\left(2\right)\mathrm{}\otimes \mathrm{SU}\left(6\right)\mathrm{}$. The mass matrix obtained from the second superconvergence relation corresponds to degenerate masses within each of the multiplets ($V=0,56\mathrm{}$) and ($V=2,56\mathrm{}$). The consequences of particle classification under the group $\mathrm{SU}\left(2\right)\mathrm{}\otimes \mathrm{SU}\left(6\right)\mathrm{}$ are enumerated.