Hamiltonian dynamics and Faddeev-Jackiw quantization of 3D gravity with a Barbero-Immirzi like parameter

TL;DR

This paper performs a detailed quantization of a 3D gravity model using Dirac and Faddeev-Jackiw methods, revealing the structure of constraints and gauge transformations, and showing the equivalence of the brackets.

Contribution

It provides a comprehensive analysis of the Bonzom-Livine 3D gravity model with a Barbero-Immirzi-like parameter, including the full constraint structure and bracket equivalence.

Findings

Faddeev-Jackiw and Dirac brackets coincide

Complete constraint and gauge structure identified

Quantization framework established for the model

Abstract

A detailed Dirac's and Faddeev-Jackiw quantization of Bonzom-Livine model describing gravity in three dimensions is performed. The full structure of the constraints, the gauge transformations and the generalized Faddeev-Jackiw brackets are found. In addition, we show that the Faddeev-Jackiw and Dirac's brackets coincide to each other. Finally we discuss some remarks and prospects.