Hamiltonian dynamics of an exotic action for gravity in three dimensions

Abstract

The Hamiltonian dynamics and the canonical covariant formalism for an exotic action in three dimensions are performed. By working with the complete phase space, we report a complete Hamiltonian description of the theory such as the extended action, the extended Hamiltonian, the algebra among the constraints, the Dirac's brackets and the correct gauge transformations. In addition, we show that in spite of exotic action and tetrad gravity with a cosmological constant give rise to the same equations of motion, they are not equivalent, in fact, we show that their corresponding Dirac's brackets are quite different. Finally, we construct a gauge invariant symplectic form which in turn represents a complete Hamiltonian description of the covariant phase space.

arXiv commentsubmitted to Annals of Physics

References in corpus (12)

• A Immirzi-like parameter for 3d quantum gravity
• A note on the Holst action, the time gauge, and the Barbero-Immirzi parameter
• Covariant canonical formalism for four-dimensional BF theory
• Self-dual gravity with topological terms
• Testing the imposition of the Spin Foam Simplicity Constraints
• A pure Dirac's canonical analysis for four-dimensional BF theories
• Hamiltonian formulation of tetrad gravity: three dimensional case
• Hamiltonian study for Chern-Simons and Pontryagin theories
• Symplectic quantization, inequivalent quantum theories, and Heisenberg's principle of uncertainty
• Hamiltonian dynamics for Einstein's action in G$\to$0 limit
• Hamiltonian dynamics of extended objects: Regge-Teitelboim model
• Remarks on 2+1 Self-dual Chern-Simons Gravity

Cited by in corpus (4)

• Hamiltonian dynamics and gauge symmetry for three-dimensional Palatini theory with cosmological constant
• Faddeev-Jackiw quantization of four dimensional BF theory
• Canonical and symplectic analysis for three dimensional gravity without dynamics
• Hamilton-Jacobi analysis for three dimensional gravity without dynamics