Canonical analysis and modified Faddeev-Jackiw approach for the Jackiw-Teitelboim model in two dimensions

Abstract

Abstract This article presents an analysis of the constraints of the Jackiw-Teitelboim model in two dimensions via the canonical analysis using the Dirac algorithm and modified Faddeev-Jackiw (FJ) approach. The analysis primarily focuses on the identification of constraints, gauge transformations, counting of physical degrees of freedom, and the generalized FJ brackets and Dirac’s brackets. To ensure gauge symmetry within the symplectic formalism and maintain consistency with the Dirac formalism, we employ the Montani-Wotzasek method, which effectively utilizes the zero modes of the symplectic matrix. Additionally, the Poincaré symmetry and diffeomorphisms in the model are identified. Finally, we present the equivalence between the generalized FJ and Dirac brackets when all the second-class constraints are treated as zero equations.