Canonical Formulation of Gravitational Teleparallelism in 2+1 Dimensions in Schwinger's Time Gauge

TL;DR

This paper develops a Hamiltonian formulation for a broad class of teleparallel gravity theories in 2+1 dimensions, revealing their constraint structure and ruling out a Newtonian limit.

Contribution

It provides a detailed Hamiltonian analysis of three-parameter teleparallel gravity theories in 2+1 dimensions, identifying a consistent reduced theory and its constraint algebra.

Findings

Constraints form a first-class set, ensuring well-defined time evolution.

The theory lacks a Newtonian limit.

Hamiltonian formulation reduces to a one-parameter family.

Abstract

We consider the most general class of teleparallel gravitational {}{}theories quadratic in the torsion tensor, in three space-time dimensions, and carry out a detailed investigation of its Hamiltonian formulation in Schwinger's time gauge. This general class is given by a family of three-parameter theories. A consistent implementation of the Legendre transform reduces the original theory to a one-parameter family of theories. By calculating Poisson brackets we show explicitly that the constraints of the theory constitute a first-class set. Therefore the resulting theory is well defined with regard to time evolution. The structure of the Hamiltonian theory rules out the existence of the Newtonian limit.