Dirac Decomposition of Wheeler-DeWitt Equation on the Bianchi Class A Models
Abstract
The Wheeler-DeWitt equation for the Bianchi Class A cosmological models is expressed generally in terms of the second-order differential equation like the Klein-Gordon equation. To obtain the positive-definite probability density, a new method extending the Dirac-Square-Root formalism, which factorizes the Wheeler-DeWitt equation into the first-order differential equation using the Pauli matrices, is investigated. The solutions to the Dirac type equation thus obtained are expressed in terms of two-component spinor form. The probability density defined by the solution is positive-definite and there is a conserved current. The newly found spin-like degree of freedom causes the universe to go through an early quantum stage of evolution with agitated anisotropy-oscillation like Zitterbewegung.
Cite
@article{arxiv.gr-qc/0101066,
title = {Dirac Decomposition of Wheeler-DeWitt Equation on the Bianchi Class A Models},
author = {Hidetomo Yamazaki},
journal= {arXiv preprint arXiv:gr-qc/0101066},
year = {2007}
}
Comments
LaTeX, 14pages, no figures