General Form of Representations of the Current Algebra in the Two-Quark Model

The algebra of vector and axial-vector charge densities at infinite momentum is solved (disregarding relativistic invariance), giving the most general form of these densities in the two-quark model of the mesons. The possibility of these solutions satisfying the angular condition for relativistic invariance is considered, and for $\mathrm{SU}\left(1\right)\mathrm{}$ currents it is found that if we cannot find a covariant solution in the simple case where the current is a sum of contributions from each quark and the mass of the two-quark system is $\mathrm{SU}\left(3\right)\mathrm{}$-independent, then we cannot find any covariant $\mathrm{SU}\left(3\right)\mathrm{}$-symmetric solution of the current algebra in this model, even with a singlet-octet mass splitting.