Discrete strings and gauge model of three confined relativistic particles

In this paper, an approach to quantizing discrete gauge models resembling bosonic strings in the Hamiltonian formulation is described. The case of three particles endowed with chiral structure and incorporating the symmetry T1 direct-product Sl(2,R)- direct-product Sl(2,R)- is analyzed both in the path-integral and operator formulations. The propagator, spectrum vacuum state and Regge trajectories are determined. The Regge trajectories are linearly rising and the spectrum is similar to one for discretized bosonic strings in space-time dimensions D ≥ 4. Possible applications to both nonperturbative string theory and bound states of relativistic quarks are outlined