Faddeev-Jackiw and Canonical Analysis of the Jackiw-Teitelboim model written as a BF theory

TL;DR

This paper analyzes the Jackiw-Teitelboim gravity model reformulated as a BF theory using Dirac and Faddeev-Jackiw formalisms, revealing its constraint structure, gauge symmetries, and equivalence of brackets.

Contribution

It provides a detailed canonical analysis of the Jackiw-Teitelboim model as a BF theory, including the full constraint structure and gauge symmetries, using both Dirac and Faddeev-Jackiw methods.

Findings

Identified the full set of constraints and gauge transformations.

Showed the equivalence of Faddeev-Jackiw and Dirac brackets.

Revealed Poincaré symmetry and diffeomorphisms in the model.

Abstract

The Jackiw-Teitelboim model written as a BF theory in two dimensions is analyzed by using the Dirac's and Faddeev-Jackiw formalism. The analysis consists in finding the full structure of the constraints, the gauge transformations, the counting of degrees of freedom and the generalized Faddeev-Jackiw brackets. The Poincar\'e symmetry and the diffeomorphisms are found. Further, we show that the Faddeev-Jackiw and Dirac's brackets coincide to each other.