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

Abstract

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]
  1. Department of Physics, National Cheng Kung University, Taiwan (China)
Publication Date:
OSTI Identifier:
22451196
Resource Type:
Journal Article
Journal Name:
Annals of Physics
Additional Journal Information:
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); Journal ID: ISSN 0003-4916
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

Citation Formats

Ita III, Eyo Eyo, E-mail: ita@usna.edu, and Soo, Chopin. Exact solutions of the Wheeler–DeWitt equation and the Yamabe construction. United States: N. p., 2015. Web. doi:10.1016/J.AOP.2015.04.016.
Ita III, Eyo Eyo, E-mail: ita@usna.edu, & Soo, Chopin. Exact solutions of the Wheeler–DeWitt equation and the Yamabe construction. United States. https://doi.org/10.1016/J.AOP.2015.04.016
Ita III, Eyo Eyo, E-mail: ita@usna.edu, and Soo, Chopin. 2015. "Exact solutions of the Wheeler–DeWitt equation and the Yamabe construction". United States. https://doi.org/10.1016/J.AOP.2015.04.016.
@article{osti_22451196,
title = {Exact solutions of the Wheeler–DeWitt equation and the Yamabe construction},
author = {Ita III, Eyo Eyo, E-mail: ita@usna.edu and Soo, Chopin},
abstractNote = {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.},
doi = {10.1016/J.AOP.2015.04.016},
url = {https://www.osti.gov/biblio/22451196}, journal = {Annals of Physics},
issn = {0003-4916},
number = ,
volume = 359,
place = {United States},
year = {Sat Aug 15 00:00:00 EDT 2015},
month = {Sat Aug 15 00:00:00 EDT 2015}
}