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

TL;DR

This paper applies the Faddeev-Jackiw symplectic method systematically to General Relativity and its extensions, providing a coherent framework for Hamiltonian analysis and clarifying previous ambiguities.

Contribution

It introduces a systematic, complete, and robust symplectic approach for Hamiltonian analysis of gravitational theories, including extensions like Brans-Dicke models.

Findings

Uncovered constraints and gauge transformations in GR and Brans-Dicke theories.

Clarified subtleties in symplectic Hamiltonian analysis of extended gravity.

Demonstrated the method's robustness and systematic nature.

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 $\omega \not= - 3/2$ 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.