On precanonical quantization of gravity

TL;DR

This paper explores a covariant precanonical quantization approach to quantum gravity, describing quantum space-time geometry with operator-valued distances and transition amplitudes, potentially impacting cosmological observations.

Contribution

It introduces a novel covariant precanonical quantization framework for gravity, linking quantum geometry to observable cosmological phenomena.

Findings

Predicts a probability distribution for cosmological spin-connection fields

Describes quantum geometry via operator-valued distances and transition amplitudes

Suggests potential observable effects on large-scale universe structures

Abstract

Precanonical quantization is based on the mathematical structures of the De Donder-Weyl Hamiltonization of field theories. The resulting formulation of quantum gravity describes the quantum geometry of space-time in terms of operator-valued distances and the transition amplitudes between the values of spin connection at different points of space-time, which obey the covariant precanonical analogue of the Schr\"odinger equation. In the context of quantum cosmology the theory predicts a probability distribution of a cosmological spin-connection field, which may have an observable impact on the large scale structures in the universe.