Abstract:
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.
Citation:
M. O. Katanaev, “Polynomial Hamiltonian form of general relativity”, TMF, 148:3 (2006), 459–494; Theoret. and Math. Phys., 148:3 (2006), 1264–1294
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