Análise Hamiltoniana de Teorias de Gravitação pela Abordagem Simplética.

Abstract

We show how to systematically apply the Faddeev-Jackiw symplectic method to General Relativity (GR), GR extensions and tetrad gravity coupled to fermions. We also develop a completely symplectic analysis for the computing of gauge symmetries and apply the results for GR. 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, in and off-shell, and the number of degrees of freedom; but the method results are also relevant for canonical quantization approaches. 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.