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

Eyo Eyo Ita; Chopin Soo

doi:10.1016/j.aop.2015.04.016

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

Eyo Eyo Ita, Chopin Soo

Department of Physics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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.

Original language	English
Pages (from-to)	80-96
Number of pages	17
Journal	Annals of Physics
Volume	359
DOIs	https://doi.org/10.1016/j.aop.2015.04.016
Publication status	Published - 2015 Aug 1

All Science Journal Classification (ASJC) codes

Physics and Astronomy(all)

Access to Document

10.1016/j.aop.2015.04.016

Fingerprint Dive into the research topics of 'Exact solutions of the Wheeler-DeWitt equation and the Yamabe construction'. Together they form a unique fingerprint.

Cite this

@article{d671a1aa20bb458584f953808305b957,

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 Schr{\"o}dinger 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.",

author = "Ita, {Eyo Eyo} and Chopin Soo",

year = "2015",

month = aug,

day = "1",

doi = "10.1016/j.aop.2015.04.016",

language = "English",

volume = "359",

pages = "80--96",

journal = "Annals of Physics",

issn = "0003-4916",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Exact solutions of the Wheeler-DeWitt equation and the Yamabe construction

AU - Ita, Eyo Eyo

AU - Soo, Chopin

PY - 2015/8/1

Y1 - 2015/8/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84928655769&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84928655769&partnerID=8YFLogxK

U2 - 10.1016/j.aop.2015.04.016

DO - 10.1016/j.aop.2015.04.016

M3 - Article

AN - SCOPUS:84928655769

VL - 359

SP - 80

EP - 96

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

ER -