Relativistic two-particle mass spectra from time-asymmetric Fokker action

The relativistic two-particle system with field-type time-asymmetric interactions is considered within the framework of manifestly covariant Hamiltonian formalism with constraints. In the second-order approximation in a coupling constant the mass-shell constraint is presented as a relation between one of the generators of SO(2, 1) and the total mass squared of the system. An algebraic quantization of the classical problem is proposed and the relativistic mass spectra for a wide range of the field-type interactions are obtained.