Mass Formula and "BrokenSU(3)" in an Associative Algebra

An associative algebra, which contains the enveloping algebra of the Poincaré group and the enveloping algebra of $\mathrm{SL}(3,c)\mathrm{}$, is considered. Its reduction with respect to irreducible representations of $\mathrm{SU}\left(3\right)\mathrm{}$ is studied and a mass formula is derived, which contains the mass formula for mesons of "broken" $\mathrm{SU}\left(3\right)\mathrm{}$ as a special case. The results are compared with experimental data.