From the DeDonder-Weyl Hamiltonian formalism to quantization of Gravity

TL;DR

This paper proposes a covariant hypercomplex Hamiltonian formalism for quantizing fields and gravity, replacing complex numbers with Clifford algebra and formulating a covariant Schrödinger-like equation.

Contribution

It introduces a novel hypercomplex extension of quantum mechanics based on the De Donder-Weyl formalism, enabling a covariant approach to quantum gravity.

Findings

Formulation of a covariant hypercomplex Schrödinger equation

Extension of quantum mechanics using space-time Clifford algebra

Initial sketch of quantization of General Relativity

Abstract

An approach to quantization of fields and gravity based on the De Donder-Weyl covariant Hamiltonian formalism is outlined. It leads to a hypercomplex extension of quantum mechanics in which the algebra of complex numbers is replaced by the space-time Clifford algebra and all space-time variables enter on equal footing. A covariant hypercomplex analogue of the Schr\"odinger equation is formulated. Elements of quantization of General Relativity within the present framework are sketched.