Hamiltonian formulation of teleparallel gravity

TL;DR

This paper develops a Hamiltonian formulation for teleparallel gravity, revealing its constraint structure and gauge symmetries, including diffeomorphisms and Lorentz transformations, and recovering the ADM algebra.

Contribution

It introduces a Hamiltonian framework for TEGR based on an anholonomy coefficient quadratic form, analyzing constraints and gauge symmetries.

Findings

Constraints form a first class algebra.

Gauge transformations include diffeomorphisms and Lorentz rotations.

ADM algebra is recovered as a sub-algebra.

Abstract

The Hamiltonian formulation of the teleparallel equivalent of general relativity (TEGR) is developed from an ordinary second-order Lagrangian, which is written as a quadratic form of the coefficients of anholonomy of the orthonormal frames (vielbeins). We analyze the structure of eigenvalues of the multi-index matrix entering the (linear) relation between canonical velocities and momenta to obtain the set of primary constraints. The canonical Hamiltonian is then built with the Moore-Penrose pseudo-inverse of that matrix. The set of constraints, including the subsequent secondary constraints, completes a first class algebra. This means that all of them generate gauge transformations. The gauge freedoms are basically the diffeomorphisms, and the (local) Lorentz transformations of the vielbein. In particular, the ADM algebra of general relativity is recovered as a sub-algebra.