Hamiltonian dynamics of an exotic action for gravity in three dimensions. (English) Zbl 1303.70019
Summary: 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.
MSC:
| 70G45 | Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics |
| 70H45 | Constrained dynamics, Dirac’s theory of constraints |
| 70S15 | Yang-Mills and other gauge theories in mechanics of particles and systems |
| 83C10 | Equations of motion in general relativity and gravitational theory |
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