ONE MODEL OF SINGULAR RELATIVISTIC LAGRANGIAN

The so-called no-interaction theorem of D. G. Currie, T. F. Jordan, E. C. Sudarshan, H. Leutwyler, G. Marmo and N. Mukunda makes it possible to construct relativistic quasiclassical particle dynamics in the pos t-Galilean approximation only. It is obtained that in this approximati on the Lagrangians are singular on some surfaces of the phase space. T hese peculiarities have different physical and mathematical nature fro m the ones studied by P. M. A, Dirac, where Hessians vanish in the who le phase-space. The dynamical properties are essentially peculiar on t he studied singular surfaces. These properties, in our opinion, can be related with some physical phenomena. In the present paper the genera l situation is first described. As the whole problem is large and diff icult we examined in detail just typical one- and two-dimensional mode ls in the second part of the paper.