Precanonical Quantum Gravity: quantization without the space-time decomposition

TL;DR

This paper introduces a covariant, background-independent approach to quantum gravity using precanonical quantization, which treats space and time equally and derives a generalized Schrödinger equation without space-time decomposition.

Contribution

It presents a novel nonperturbative, covariant quantization method for gravity based on the De Donder-Weyl Hamiltonian formulation, avoiding traditional space-time splitting.

Findings

Derivation of a covariant generalized Schrödinger equation for gravity.

Introduction of a bootstrap condition linking quantum averages to classical geometry.

Demonstration of background independence in the quantization approach.

Abstract

A nonpertubative approach to quantum gravity using precanonical field quantization originating from the covariant De Donder-Weyl Hamiltonian formulation which treats space and time variables on equal footing is presented. A generally covariant ``multi-temporal'' generalized Schroedinger equation on the finite dimensional space of metric and space-time variables is obtained. An important ingredient of the formulation is the ``bootstrap condition'' which introduces a classical space-time geometry as an approximate concept emerging as the quantum average in a self-consistent with the underlying quantum dynamics manner. An independence of the theory from an arbitrarily fixed background is ensured in this way. The prospects and unsolved problems of precanonical quantization of gravity are outlined.