Geodesic
Polynomial Hamiltonian form of general relativity
Teoretičeskaâ i matematičeskaâ fizika, Tome 148 (2006) no. 3, pp. 459-494 Cet article a éte moissonné depuis la source Math-Net.Ru

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The 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. We propose a new expression for the generating functional for the Green's functions. We show that the Dirac bracket defines a degenerate Poisson structure on a manifold and the second-class constraints are the Casimir functions with respect to this structure. As an application of the new variables, we consider the Friedmann universe.
Keywords: general relativity, Hamiltonian formalism. 
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M. O. Katanaev. Polynomial Hamiltonian form of general relativity. Teoretičeskaâ i matematičeskaâ fizika, Tome 148 (2006) no. 3, pp. 459-494. http://geodesic.mathdoc.fr/item/TMF_2006_148_3_a7/

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