On the Faddeev-Jackiw Symplectic Framework for Topologically Massive Gravity
The dynamical structure of topologically massive gravity in the context of the Faddeev-Jackiw approach is studied. We present a detailed analysis of the constraints and we show that this formalism is equivalent and more economical than Dirac’s method. In particular, we identify the complete set of constraints of the theory, from which the number of physical degrees of freedom is explicitly computed. Furthermore, in order to obtain all the generalized Faddeev-Jackiw brackets an appropriate gauge-fixing procedure is introduced and we prove that the generalized Faddeev-Jackiw brackets and the Dirac ones coincide to each other. Finally, the similarities and advantages between Faddeev-Jackiw method and Dirac’s formalism are discussed.