Covariant Hamiltonian quantization of teleparallel equivalents to general relativity

TL;DR

This paper develops a covariant Hamiltonian framework for teleparallel gravity, avoiding primary constraints and proposing a Tomonaga-Schwinger-type evolution equation for nonperturbative quantum gravity.

Contribution

It introduces a novel covariant Hamiltonian formulation for teleparallel equivalents of general relativity, enabling a new approach to quantum gravity without a preferred time.

Findings

Hamiltonian densities are non-singular and constraint-free in teleparallel gravity.

A Tomonaga-Schwinger-type equation is formulated for hypersurface-independent evolution.

The framework offers a classically equivalent, nonperturbative quantum gravity approach.

Abstract

A covariant Hamiltonian formulation generalizing De Donder-Weyl mechanics is constructed with field strengths as velocity fields. Since the teleparallel equivalents to general relativity are quadratic in field strengths, the field-strength Hamiltonian densities are non-singular and avoid primary constraints specifically from Legendre degeneracy. In contrast, canonical general relativity and the Wheeler-DeWitt equation have a frozen formalism due to Hamiltonian constraints, while hypersurface deformations give refoliation gauge transformations. We introduce a Tomonaga-Schwinger-type equation without a preferred time coordinate by combining the generalized multisymplectic geometry with covariant phase space methods. Point-splitting regularization with renormalized hypersurface deformation generators is proposed as a candidate for hypersurface-dependent evolution. While ultraviolet divergences, operator domain issues, and anomaly freedom are still open problems, we provide a new framework for exploring nonperturbative quantum gravity that is classically equivalent to general relativity.