Reparametrization-invariant Hamiltonian formalism in the general theory ofrelativity

A method is proposed that is appropriate for resolving the Hamiltonian cons traint and which leads to a reparametrization-invariant reduced theory spec ified by a well-defined nonzero local Hamiltonian. This method is based on introducing a global (dependent only on time) conformal variable. The physi cal and geometric meaning of the variables in the reduced action functional is investigated. It is shown that, within the theory, the method of small perturbations is self-consistent. It is demonstrated that, in the theory of gravity, there are no wavelike excitations that make a negative contributi on to the Hamiltonian. From an analysis of the reduced classical theory in the linear approximation, it follows that, at the first instants from the b irth of the Universe, the extremely rigid equation of state appeared to be the effective equation of the state of gravity matter. (C) 2001 MAIK "Nauka /Interperiodica".