The time-asymmetric Fokker-type integrals and the relativistic mechanics on the light cone

The class of two-particle relativistic model which are described by the time-asymmetric Fokker-type integral of general form is considered. The manifestly covariant description of such models is constructed in the framework of the canonical formalism with constrains. By means of certain gauge fixing, the time-asymmetric models are reduced to the Bakamjian-Thomas model supplemented by a space-time interpretation. The corresponding two-body problem is reduced to quadratures. (author)