Hamiltonian dynamics and gauge symmetry for three-dimensional Palatini theory with cosmological constant

Abstract

A pure Dirac's framework for 3D Palatini's theory with cosmological constant is performed. By considering the complete phase space, we find out the full structure of the constraints, and their corresponding algebra is computed explicitly. We report that in order to obtain a well defined algebra among the constraints, the gauge group must be $SO(2,1)$. In addition, we obtain the extended action, the extended Hamiltonian, the fundamental gauge symmetry, and the Dirac brackets of the theory. Finally, we compare our results with those reported in the literature.

References in corpus (3)

• Hamiltonian study for Chern-Simons and Pontryagin theories
• Hamiltonian dynamics of extended objects: Regge-Teitelboim model
• Hamiltonian dynamics of an exotic action for gravity in three dimensions

Cited by in corpus (7)

• Faddeev-Jackiw quantization of four dimensional BF theory
• Three-dimensional Background Field Gravity: A Hamilton-Jacobi analysis
• On the Faddeev-Jackiw Symplectic Framework for Topologically Massive Gravity
• Gauge symmetry and constraints structure in topologically massive AdS gravity: A symplectic viewpoint
• Dirac's and Generalized Faddeev-Jackiw brackets for Einstein's theory in G $\to 0$ limit
• Hamiltonian analysis of metric-affine-$R^2$ theory
• Constrained dynamics of two interacting relativistic particles in the Faddeev-Jackiw symplectic framework