Quantum gravity equation in Schrodinger form in minisuperspace description

Citation
S. Biswas et al., Quantum gravity equation in Schrodinger form in minisuperspace description, GEN RELAT G, 32(11), 2000, pp. 2167-2187
Citations number
33
Categorie Soggetti
Physics
Journal title
GENERAL RELATIVITY AND GRAVITATION
ISSN journal
00017701 → ACNP
Volume
32
Issue
11
Year of publication
2000
Pages
2167 - 2187
Database
ISI
SICI code
0001-7701(200011)32:11<2167:QGEISF>2.0.ZU;2-M
Abstract
We start from the classical Hamiltonian constraint of general relativity to obtain the Einstein-Hamiltonian-Jacobi equation. We obtain a time paramete r prescription demanding that geometry itself determines the time, not the matter field, such that the time so defined being equivalent to the time th at enters into the Schrodinger equation. Using a semiclassical approximatio n we obtain an equation for quantum gravity in Schrodinger form containing time. We restrict ourselves to a minisuperspace description. Unlike matter held equation our equation is equivalent to the Wheeler-DeWitt equation in the sense that our solutions reproduce also the wavefunction of the Wheeler -DeWitt equation provided one evaluates the normalization constant accordin g to the wormhole dominance proposal recently proposed by us.