On precanonical quantization of gravity in spin connection variables

TL;DR

This paper explores a novel precanonical quantization approach for gravity using spin connection variables, resulting in a covariant Schrödinger equation that offers a new quantum perspective on space-time geometry, demonstrated through a quantum cosmology toy model.

Contribution

It introduces a precanonical quantization method for gravity in spin connection variables, leading to a covariant quantum dynamics framework distinct from traditional approaches.

Findings

Derivation of a covariant Schrödinger equation for gravity

Application to a quantum cosmology toy model

New insights into quantum space-time geometry

Abstract

The basics of precanonical quantization and its relation to the functional Schr\"odinger picture in QFT are briefly outlined. The approach is applied to quantization of Einstein's gravity in vielbein and spin connection variables and leads to a quantum dynamics described by the covariant Schr\"odinger equation for the transition amplitudes on the bundle of spin connection coefficients over the space-time, that yields a novel quantum description of space-time geometry. A toy model of precanonical quantum cosmology based on the example of flat FLRW universe is considered.