Geodesic
Polynomial Hamiltonian form of general relativity
Teoretičeskaâ i matematičeskaâ fizika, Tome 148 (2006) no. 3, pp. 459-494

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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. 
@article{TMF_2006_148_3_a7,
     author = {M. O. Katanaev},
     title = {Polynomial {Hamiltonian} form of general relativity},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {459--494},
     publisher = {mathdoc},
     volume = {148},
     number = {3},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2006_148_3_a7/}
}
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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/