Canonical and symplectic analysis for three dimensional gravity without dynamics

TL;DR

This paper performs a comprehensive Hamiltonian and symplectic analysis of three-dimensional gravity without dynamics, clarifying the structure of constraints and brackets, and comparing two formalisms for constrained systems.

Contribution

It provides a detailed comparison of Dirac and Faddeev-Jackiw formalisms applied to three-dimensional gravity without dynamics, including explicit calculations of constraints and brackets.

Findings

Complete structure of constraints identified

Dirac and Faddeev-Jackiw brackets shown to coincide

Advantages of Faddeev-Jackiw approach discussed

Abstract

In this paper a detailed Hamiltonian analysis of three-dimensional gravity without dynamics proposed by V. Hussain is performed. We report the complete structure of the constraints and the Dirac brackets are explicitly computed. In addition, the Faddeev-Jackiw symplectic approach is developed; we report the complete set of Faddeev-Jackiw constraints and the generalized brackets, then we show that the Dirac and the generalized Faddeev-Jackiw brackets coincide to each other. Finally, the similarities and advantages between Faddeev-Jackiw and Dirac's formalism are briefly discussed.