Relativistic Bound State Solutions of a Two-Dimensional Fermion Model with Color SU(3) Symmetry

We implement color SU(3) symmetry on a relativistic two-dimensional fermion model proposed by Glockle, Nogami and Fukui (GNF). We find that it is possible to construct solutions for several multiplets of two and three particles by using the solutions for the GNF model. Though our model is based on the single-particle theory (i.e., the model does not contain any anti-particles), we regard a particle belonging to 3 as an anti-particle while the particles belong to 3 representation of the SU(3) group. There are conditions for the coupling constant that must be satisfied in order that a solution is acceptable as a physical bound state. We construct bound state solutions of 3 for a particle-particle pair, 1 for a particle-anti-particle pair and 1 for a three-particle system. We find that the singlet states form the tightest bound states among these solutions. We believe that our result provides some useful information for understanding quark confinement.