Description of the widths and spectra of the bound states of two relativistic fermions

A formalism is constructed for the relativistic description of a system of two spin $1/2$ particles on the basis of a two-particle three-dimensional covariant quasipotential equation. In a relativistic configuration representation, this equation with one-boson exchange potential is reduced to a system of partial difference equations, this being the relativistic analog of the nonrelativistie Hamada–Johnston system. The WKB method is used to solve the problem of the mass spectrum of the bound states. The exact solution of the relativistic Coulomb two-body problem is used to obtain expressions for the widths of leptonic decays in the quark model.