Formalism of classical Cartan mechanics as a basis to construct unified field theory

Abstract

Eearlier the theory has been developed describing the motion of a particle and its interaction with physical fields on the basis of the symplectic metric of extended phase space-time. The corresponding held-equations are obtained in the framework of the formalism of the Kalutsa fifth-dimensional theory. It is evident that such a theory is not fully consecutive Here a more general approach is developed when not only equations of motion and interaction of particles but also the gravitational fields follow from the symplectic metric