Fokker-Type Confinement Models from Effective Lagrangian in Classical Yang-Mills Theory

Abelian potentials of pointlike moving sources are obtained from the nonstandard theory of Yang--Mills field. They are used for the construction of the time-symmetric and time-asymmetric Fokker-type action integrals describing the dynamics of two-particle system with confinement interaction. The time-asymmetric model is reformulated in the framework of the Hamiltonian formalism. The corresponding two-body problem is reduced to quadratures. The behaviour of Regge trajectories is estimated within the semiclassical consideration.