Hamiltonian Analysis of Gravitation Theories through the Symplectic Approach.

Name: Mariniel Souza Galvão Junior
Type: PhD thesis
Publication date: 17/06/2021
Advisor:

Namesort descending Role
Davi Cabral Rodrigues Advisor *

Examining board:

Namesort descending Role
Davi Cabral Rodrigues Advisor *
Galen Mihaylov Sotkov Internal Examiner *
Júlio César Fabris Internal Examiner *
Marcelo Santos Guimarães External Examiner *
Nelson Pinto Neto External Examiner *
Roldão da Rocha Junior External Examiner *

Summary: 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.

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