Hamiltonian structure of three-dimensional gravity in Vielbein formalism

TL;DR

This paper analyzes the Hamiltonian structure of three-dimensional gravity theories in the Vielbein formalism, revealing new constraints and clarifying degrees of freedom in topological and massive gravity models.

Contribution

It introduces a novel feature of constraints arising from determinant factorization and compares linearized and original models' Hamiltonian structures.

Findings

Identification of new constraints due to determinant factorization

Determination of the degrees of freedom in each model

Comparison of linearized and original Hamiltonian structures

Abstract

Considering Chern-Simons like gravity theories in three dimensions as first order systems, we analyze the Hamiltonian structure of three theories Topological massive gravity, New massive gravity, and Zwei-Dreibein Gravity.We show that these systems demonstrate a new feature of the constrained systems in which a new kind of constraints emerge due to factorization of determinant of the matrix of Poisson brackets of constraints. We find the desired number of degrees of freedom as well as the generating functional of local Lorentz transformations and diffeomorphism through canonical structure of the system. We also compare the Hamiltonian structure of linearized version of the considered models with the original ones.