Exact solutions of the Wheeler–DeWitt equation and the Yamabe construction

Journal Article · Sat Aug 15 00:00:00 EDT 2015 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2015.04.016· OSTI ID:22451196

Soo, Chopin ^[1]

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1. Department of Physics, National Cheng Kung University, Taiwan (China)

Exact solutions of the Wheeler–DeWitt equation of the full theory of four dimensional gravity of Lorentzian signature are obtained. They are characterized by Schrödinger wavefunctionals having support on 3-metrics of constant spatial scalar curvature, and thus contain two full physical field degrees of freedom in accordance with the Yamabe construction. These solutions are moreover Gaussians of minimum uncertainty and they are naturally associated with a rigged Hilbert space. In addition, in the limit the regulator is removed, exact 3-dimensional diffeomorphism and local gauge invariance of the solutions are recovered.

• OSTI ID: 22451196
• Journal Information: Annals of Physics, Vol. 359; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DEGREES OF FREEDOM
EXACT SOLUTIONS
FOUR-DIMENSIONAL CALCULATIONS
GAUGE INVARIANCE
GRAVITATION
HILBERT SPACE
METRICS
QUANTIZATION
SCHROEDINGER EQUATION