On the Faddeev–Jackiw symplectic framework for topologically massive gravity

Abstract

The dynamical structure of topologically massive gravity in the context of the Faddeev–Jackiw symplectic approach is studied. It is shown that this method allows us to avoid some ambiguities arising in the study of the gauge structure via the Dirac formalism. In particular, the complete set of constraints and the generators of the gauge symmetry of the theory are obtained straightforwardly via the zero modes of the symplectic matrix. In order to obtain the generalized Faddeev–Jackiw brackets and calculate the local physical degrees of freedom of this model, an appropriate gauge-fixing procedure is introduced. Finally, the similarities and relative advantages between the Faddeev–Jackiw method and Dirac’s formalism are briefly discussed.