Symmetries of the Fokker-Type Relativistic Mechanics in Various Forms of Dynamics

Abstract

The single-time nonlocal Lagrangians corresponding to the Fokker-type action integrals are obtained in arbitrary form of relativistic dynamics. The symmetry conditions for such Lagrangians under an arbitrary Lie group acting on the Minkowski space are formulated in various forms of dynamics. An explicit expression for the integrals of motion corresponding to the Poincaré invariance is derived.