Diffeomorphism Invariance in the Hamiltonian formulation of General Relativity

Details Diffeomorphism Invariance in the Hamiltonian formulation of General Relativity Diffeomorphism Invariance in the Hamiltonian formulation of General Relativity

2008-08-19

arxiv.org/abs/0808.2623v1

Phys.Lett.A372:5101-5105,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages

Scientific paper

10.1016/j.physleta.2008.05.081

It is shown that when the Einstein-Hilbert Lagrangian is considered without any non-covariant modifications or change of variables, its Hamiltonian formulation leads to results consistent with principles of General Relativity. The first-class constraints of such a Hamiltonian formulation, with the metric tensor taken as a canonical variable, allow one to derive the generator of gauge transformations, which directly leads to diffeomorphism invariance. The given Hamiltonian formulation preserves general covariance of the transformations derivable from it. This characteristic should be used as the crucial consistency requirement that must be met by any Hamiltonian formulation of General Relativity.

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