Gravitação Canônica no Formalismo Simplético

Abstract

The Hamiltonian formalism in theories of gravitation, also known as ADM formalism, is used in a wide variety of aplications, from obtaining numerical solutions to searching quantum gravity theories. Despite various non-trivial and typical particularities of General Relativity, it is known that the ADM formalism may be understood from Dirac’s treatment of constrained systems. In this work is presented a review of Dirac’s method, a review of the symplectic method, which constitutes another method of Hamiltonian function analysis, a review of the ADM formalism and, finally, we present a new development of the ADM formalism from the symplectic method. Aplications for General Relativity and Brans-Dicke are presented here in details.