Symplectic analysis of three dimensional Abelian topological gravity

TL;DR

This paper applies the Faddeev-Jackiw method to analyze three-dimensional Abelian topological gravity, demonstrating its equivalence to Dirac's approach and explicitly computing the physical degrees of freedom.

Contribution

It provides a detailed Faddeev-Jackiw quantization of Abelian topological gravity, showing its advantages over Dirac's method and analyzing the theory at the chiral point.

Findings

Faddeev-Jackiw and Dirac brackets coincide

Complete set of constraints identified

Physical degrees of freedom explicitly computed

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.