The Hamiltonian in Covariant Theory of Gravitation

Abstract

In the framework of covariant theory of gravitation the Euler-Lagrange equations are written and equations of motion are determined by using the Lagrange function, in the case of small test particle and in the case of continuously distributed matter. From the Lagrangian transition to the Hamiltonian was done, which is expressed through three-dimensional generalized momentum in explicit form, and also is defined by the 4-velocity, scalar potentials and strengths of gravitational and electromagnetic fields, taking into account the metric. The definition of generalized 4-velocity, and the description of its application to the principle of least action and to Hamiltonian is done. The existence of a 4-vector of the Hamiltonian is assumed and the problem of mass is investigated. To characterize the properties of mass we introduce three different masses, one of which is connected with the rest energy, another is the observed mass, and the third mass is determined without taking into account the energy of macroscopic fields. It is shown that the action function has the physical meaning of the function describing the change of such intrinsic properties as the rate of proper time and rate of rise of phase angle in periodic processes.

Key words: Euler-Lagrange equations; Lagrangian; Hamiltonian; Generalized momentum; Generalized 4-velocity; Equations of motion