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Polynomial Hamiltonian form of General Relativity

M. O. Katanaev
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Abstract

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.

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M. O. Katanaev. 2006-09-06. Polynomial Hamiltonian form of General Relativity. https://doi.org/10.1007/s11232-006-0116-3

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