Meson and Baryon Resonances in RelativisticSU(6)

Abstract

The relativistic $\mathrm{SU}\left(6\right)\mathrm{}$ supermultiplets which can be constructed from two quarks and two antiquarks, three quarks, or four quarks and one antiquark are examined as possible candiates for the classification of meson and baryon resonances. The multiplets can be labeled either by the $\mathrm{SU}\left(12\right)\mathrm{}$ formalism or by the $U\left(6\right)\mathrm{}\times U\left(6\right)\mathrm{}$ group of Dashen and Gell-Mann; the two groups lead to equivalent classifications. Those static $\mathrm{SU}\left(6\right)\mathrm{}$ multiplets within a given $\mathrm{SU}\left(12\right)\mathrm{}$ multiplet which represent physical particles (i.e., satisfy Bargmann-Wigner equations) are just the states having the maximal eigenvalue of ${\gamma }_0$ in the $\mathrm{SU}\left(12\right)\mathrm{}$ multiplet. These constitute a representation of the Dashen-Gell-Mann $U\left(6\right)\mathrm{}\times U\left(6\right)\mathrm{}$ subgroup of $U\left(12\right)\mathrm{}$ which commutes with ${\gamma }_0$. Applications to specific resonances are discussed.