An Approach to the Problem of Bound States. I

An approach, which has some connection with the Tamm-Dancoff method, is proposed for treating the problem of bound states. In the framework of the relativistic field theory, the particle-antiparticle two-body system is discussed in the vector four-Fermion interaction containing form factor. The integral equations in the momentum representation are derived for all singlet and triplet states, and a partial wave analysis is made. The solutions are obtained for all the possible bound states (1S0, SP0, SP1 and 3S1 +3D1) in the special case of contact interaction. An unfamiliar'-feature appears in the 1S0 state