Relativistic two-body system in (1+1) dimensions

The relativistic two-body system in (1 + 1)-dimensional quantum electrodyna mics is studied. It is proved that the eigenvalue problem for the two-body Hamiltonian without the self-interaction terms reduces to the problem of so lving a one-dimensional stationary Schrodinger-type equation with an energy -dependent effective potential which includes the delta-functional and inve rted oscillator parts. The conditions determining the metastable energy spe ctrum are derived, and the energies and widths of the metastable levels are estimated in the limit of large particle masses. The effects of the self-i nteraction are discussed.