Precanonical Perspective in 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.

4 pages, LaTeX, espcrc2.sty. Based on the talk at the Third Meeting on Constrained Dynamics and Quantum Gravity QG99 (Villasimius, Sardinia, Italy, Sept. 13-17, 1999). To appear in Nucl. Phys. B Proc. Suppl. (2000). Minor misprints in the version in print corrected

References in corpus (3)

• Canonical Structure of Classical Field Theory in the Polymomentum Phase Space
• On Field Theoretic Generalizations of a Poisson Algebra
• DeDonder-Weyl theory and a hypercomplex extension of quantum mechanics to field theory

Cited by in corpus (10)

• Multisymplectic Lagrangian and Hamiltonian Formalisms of Classical Field Theories
• Precanonical Quantization and the Schroedinger Wave Functional
• Precanonical Quantum Gravity: quantization without the space-time decomposition
• De Donder-Weyl Hamiltonian formulation and precanonical quantization of vielbein gravity
• Precanonical quantization and the Schrödinger wave functional revisited
• On the precanonical structure of the Schrödinger wave functional
• Schrödinger Functional of a Quantum Scalar Field in Static Space-Times from Precanonical Quantization
• Precanonical structure of the Schrödinger wave functional in curved space-time
• Clifford Algebraic approach to the De Donder-Weyl Hamiltonian theory
• p-Mechanics and De Donder-Weyl Theory