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

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.
Authors:
 [1] ;  [2]
  1. Physics Department, US Naval Academy, Annapolis, MD (United States)
  2. Department of Physics, National Cheng Kung University, Taiwan (China)
Publication Date:
OSTI Identifier:
22451196
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics; Journal Volume: 359; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DEGREES OF FREEDOM; EXACT SOLUTIONS; FOUR-DIMENSIONAL CALCULATIONS; GAUGE INVARIANCE; GRAVITATION; HILBERT SPACE; METRICS; QUANTIZATION; SCHROEDINGER EQUATION