Precanonical Perspective in Quantum Gravity

TL;DR

This paper explores a background-independent approach to quantum gravity using precanonical quantization based on the De Donder-Weyl covariant Hamiltonian formulation, deriving classical geometry elements from quantum dynamics.

Contribution

It introduces a novel precanonical quantization method for general relativity that does not rely on a fixed background, connecting classical geometry with quantum metric dynamics.

Findings

Derivation of classical geometry elements from quantum metric dynamics

Development of a Dirac-like wave equation for quantum gravity

Background-independent formulation of quantum gravity

Abstract

Quantization of general relativity in metric variables using ``precanonical'' quantization based on the De Donder-Weyl covariant Hamiltonian formulation is outlined. Elements of classical geometry needed to formulate the (Dirac-like) wave equation emerge from a self-consistency with the underlying quantum dynamics of the metric. In this sense the formulation can be viewed as independent from an arbitrarily fixed background.