Nonlinear quantum gravity on the constant mean curvature foliation

Abstract

A new approach to quantum gravity is presented based on a nonlinear quantization scheme for canonical field theories with an implicitly defined Hamiltonian. The constant mean curvature foliation is employed to eliminate the momentum constraints in canonical general relativity. It is, however, argued that the Hamiltonian constraint may be advantageously retained in the reduced classical system to be quantized. This permits the Hamiltonian constraint equation to be consistently turned into an expectation value equation on quantization that describes the scale factor on each spatial hypersurface characterized by a constant mean exterior curvature. This expectation value equation augments the dynamical quantum evolution of the unconstrained conformal three-geometry with a transverse traceless momentum tensor density. The resulting quantum theory is inherently nonlinear. Nonetheless, it is unitary and free from a nonlocal and implicit description of the Hamiltonian operator. Finally, by imposing additional homogeneity symmetries, a broad class of Bianchi cosmological models are analyzed as nonlinear quantum minisuperspaces in the context of the proposed theory.

14 pages. Classical and Quantum Gravity (To appear)

References in corpus (9)

• Dynamical Reduction Models
• Quantum Gravity: a Progress Report
• Do we really understand quantum mechanics?
• Functional Evolution of Free Quantum Fields
• Midi-superspace Models of Canonical Quantum Gravity
• Evolutionary Laws, Initial Conditions, and Gauge Fixing in Constrained Systems
• Involution and Constrained Dynamics I: The Dirac Approach
• An action principle for the quantization of parametric theories and nonlinear quantum cosmology
• A nonlinear quantum model of the Friedmann universe

Cited by in corpus (6)

• Relational Particle Models. II. Use as toy models for quantum geometrodynamics
• Conformal geometrodynamics: True degrees of freedom in a truly canonical structure
• A fundamental threat to quantum cryptography: gravitational attacks
• Informal Resource Letter - Nonlinear quantum mechanics on arXiv up to August 2004
• Towards conformal loop quantum gravity
• The conformal factor in the parameter-free construction of spin-gauge variables for gravity