Towards Precanonical Quantum Teleparallel Gravity

TL;DR

This paper explores the quantization of teleparallel gravity using the De Donder-Weyl Hamiltonian approach, deriving a covariant Schrödinger equation and linking operator ordering to the cosmological constant.

Contribution

It introduces a precanonical quantization framework for TEGR, deriving operator representations and a covariant Schrödinger equation from the polysymplectic formulation.

Findings

Operator ordering affects the Hamiltonian operator.

The cosmological constant emerges naturally from the quantization process.

Estimated value of the cosmological constant aligns with observations.

Abstract

Quantization of the teleparallel equivalent of general relativity (TEGR) is discussed from the perspective of the space-time symmetric De Donder-Weyl (DW) Hamiltonian formulation with constraints and its quantization called precanonical quantization. The representations of operators and the covariant Schr\"odinger equation for TEGR are obtained from the quantization of generalized Dirac brackets calculated according to the analysis of constraints within the polysymplectic formulation of the DW Hamiltonian theory. We argue that the appropriate treatment of the operator ordering and the generalized Hermicity of operators results in an additional $c$-number term in the DW Hamiltonian operator which is identified with the cosmological constant and estimated to be consistent with its observed value.