Faddeev-Jackiw quantization of an Abelian and non-Abelian exotic action for gravity in three dimensions

TL;DR

This paper applies the Faddeev-Jackiw quantization method to Abelian and non-Abelian exotic gravity actions in three dimensions, deriving constraints, gauge transformations, brackets, and confirming consistency with canonical analysis.

Contribution

It provides a detailed Faddeev-Jackiw quantization framework for exotic gravity actions in three dimensions, including constraints and brackets, and compares results with canonical methods.

Findings

Faddeev-Jackiw brackets match Dirac brackets

Constraints and gauge transformations are explicitly derived

Physical degrees of freedom are counted

Abstract

A detailed Faddeev-Jackiw quantization of an Abelian and non-Abelian exotic action for gravity in three dimensions is performed. We obtain for the theories under study the constraints, the gauge transformations, the generalized Faddeev-Jackiw brackets and we perform the counting of physical degrees of freedom. In addition, we compare our results with those found in the literature where the canonical analysis is developed, in particular, we show that both the generalized Faddeev-Jackiw brackets and Dirac's brackets coincide to each other. Finally we discuss some remarks and prospects.