TY - JOUR

T1 - Nonlinear quantum gravity on the constant mean curvature foliation

AU - Wang, Charles H.T.

N1 - I take this opportunity to express gratitude to many colleagues for enlightening conversations and insightful comments on this work, especially to Profs Arthur E Fischer, Chris J Isham, Karel V Kuchař, Niall O Murchadha and Robin W Tucker and Dr Edward Anderson. The research programme has benefited from partial support from the EPSRC and Centre for Fundamental Physics, CCLRC.

PY - 2004/12/3

Y1 - 2004/12/3

N2 - 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 analysed as nonlinear quantum minisuperspaces in the context of the proposed theory.

AB - 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 analysed as nonlinear quantum minisuperspaces in the context of the proposed theory.

UR - http://www.scopus.com/inward/record.url?scp=11944272917&partnerID=8YFLogxK

U2 - 10.1088/0264-9381/22/1/003

DO - 10.1088/0264-9381/22/1/003

M3 - Article

AN - SCOPUS:11944272917

VL - 22

SP - 33

EP - 45

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

SN - 0264-9381

IS - 1

ER -