From the DeDonder-Weyl Hamiltonian formalism to quantization of Gravity

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 Schrödinger equation is formulated. Elements of quantization of General Relativity within the present framework are sketched.

arXiv comment10pp, LaTeX, uses sprocl.sty. To appear in the Proceedings of the International Seminar on Mathematical Cosmology, Potsdam, Mar-Apr 98, ed. H.-J. Schmidt and M. Rainer, World Scientific, Singapore 1998

Cited by in corpus (8)

• Precanonical Quantum Gravity: quantization without the space-time decomposition
• Precanonical quantization and the Schrödinger wave functional revisited
• Quantization of Gravity: Yet Another Way
• p-Brane Quantum Mechanical Wave Equations
• Towards a "pre-canonical" quantization of gravity without the space+time decomposition
• Schrödinger Functional of a Quantum Scalar Field in Static Space-Times from Precanonical Quantization
• p-Mechanics and De Donder-Weyl Theory
• Tales from the prehistory of Quantum Gravity. Léon Rosenfeld's earliest contribution