Towards Precanonical Quantum Teleparallel Gravity

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.