Symplectic analysis of three-dimensional Abelian topological gravity

Abstract

A detailed Faddeev-Jackiw quantization of an Abelian topological gravity is performed; 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. We prove that the generalized Faddeev-Jackiw brackets and the Dirac ones coincide to each other. Moreover, we perform the Faddeev-Jackiw analysis of the theory at the chiral point, and the full set of constraints and the generalized Faddeev-Jackiw brackets are constructed. Finally we compare our results with those found in the literature and we discuss some remarks and prospects.

Canonical analysis and modified Faddeev-Jackiw approach for the Jackiw-Teitelboim model in two dimensions

“…However, an extension of the symplectic approach BW has been proposed by [22,23]. The modified FJ symplectic and the symplectic approach BW formalism have been employed to investigate various theories, such as the quantization of massive non-Abellian Yang-Mills fields [24], quantization of the electromagnetic field [25], quantization of an Abelian and non-Abelian exotic action for gravity in three dimensions [26], topologically massive gravity (TMG) [27], the Bonzom-Livine action [28], the abelian analog version of TMG theory at the chiral point [29], as well as the four-dimensional General Relativity and its extensions [30].…”