  Phase space of General Relativity is extended to a Poisson manifold by
inclusion of the determinant of the metric and conjugate momentum as additional
independent variables. As a result, the action and the constraints take a
polynomial form. New expression for the generating functional for the Green
functions is proposed. We show that the Dirac bracket defines degenerate
Poisson structure on a manifold, and a second class constraints are the Casimir
functions with respect to this structure. As an application of the new
variables, we consider the Friedmann universe.
