ADM-like Hamiltonian formulation of gravity in the teleparallel geometry

TL;DR

This paper develops a new Hamiltonian formulation of the Teleparallel Equivalent of General Relativity (TEGR) using an ADM-like decomposition, aiming to facilitate its canonical quantization without gauge fixing.

Contribution

It introduces a novel Hamiltonian framework for TEGR based on differential forms and an ADM-like split, providing a foundation for quantum gravity research.

Findings

Complete set of phase space constraints presented

Constraint algebra derived and analyzed

Formulation expressed in differential forms

Abstract

We present a new Hamiltonian formulation of the Teleparallel Equivalent of General Relativity (TEGR) meant to serve as the departure point for canonical quantization of the theory. TEGR is considered here as a theory of a cotetrad field on a spacetime. The Hamiltonian formulation is derived by means of an ADM-like 3+1 decomposition of the field and without any gauge fixing. A complete set of constraints on the phase space and their algebra are presented. The formulation is described in terms of differential forms.