BOUND-STATE PROBLEM IN THE LIGHT-FRONT TAMM-DANCOFF APPROXIMATION - NUMERICAL STUDY IN 1+1 DIMENSIONS

Numerical solutions to the two-fermion bound-state problem in the (1 + 1)-dimensional Yukawa model are presented within the lowest-order light-front Tamm-Dancoff approximation (i.e., keeping only two-fermion and two-fermion-one-boson sectors). Our motivation is twofold. First, we want to understand the dynamics of the model from the very-weak-coupling domain, where the system is governed by nonrelativistic dynamics, to moderate and strong-coupling domains where retardation and self-energy effects become important. Second, we want to develop techniques for solving coupled Tamm-Dancoff integral equations, in particular, methods that can be generalized to higher-order Tamm-Dancoff approximations. To achieve the first goal we first simplify the problem considerably (from a numerical point of view) by the explicit elimination of the higher Fock-space sector. The resulting integral equation, whose kernel depends upon the invariant mass of the state, is solved for the coupling constant, for a given set of the invariant mass and fermion and boson mass parameters. To achieve the second goal we solve the coupled set of equations using both basis functions and direct-discretization techniques. Results from these more general techniques are compared with the explicit-elimination method.