On the Hamiltonian form of the Einstein equations for gravitational field

TL;DR

This paper demonstrates that Einstein's gravitational equations are equivalent to the canonical equations derived from the Dirac-Schwinger Hamiltonian in Faddeev variables, establishing a canonical Hamiltonian formulation of gravity.

Contribution

It shows the equivalence between Einstein equations and canonical equations in Faddeev variables, providing a Hamiltonian framework for gravitational fields.

Findings

Einstein equations rewritten in canonical variables.

Time derivatives of generalized momenta calculated using Poisson brackets.

Equivalence between Einstein equations and Hamiltonian canonical equations confirmed.

Abstract

It is shown that Einstein gravitational equations and canonical equations following from the Dirac-Schwinger Hamiltonian in the Faddeev variables coincide. For proving of this at first, the Einstein equations has been rewritten in canonical variables, and after this, the time derivative of the generalized momenta of the gravitational field in Faddeev form has been calculated using canonical Poisson brackets. The results coincide.