Hamiltonian analysis of General Relativity and extended gravity from the iterative Faddeev-Jackiw symplectic approach

Abstract

We show how to systematically apply the Faddeev-Jackiw symplectic method to General Relativity (GR) and to GR extensions. This provides a new coherent frame for Hamiltonian analyses of gravitational theories. The emphasis is on the classical dynamics, uncovering the constraints, the gauge transformations and the number of degrees of freedom; but the method results are also relevant for canonical quantization approaches. We illustrate the method with three applications: GR and to two Brans-Dicke cases (the standard case $\omega \ne -3/2$ and the case with one less degree of freedom, $\omega =-3/2$). We clarify subtleties of the symplectic approach and comment on previous symplectic-based Hamiltonian analyses of extended theories of gravity, pointing out that the present approach is systematic, complete and robust.

31 pages. v2: added comments. Version to appear in Phys.Rev.D

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