Quantum billiards in multidimensional models with fields of forms
Abstract
Bianchi type I cosmological model in (n+1)-dimensional gravity with several forms is considered. When the electric non-composite brane ansatz is adopted, the Wheeler-DeWitt (WDW) equation for the model, written in a conformally covariant form, is analyzed. Under certain restrictions, asymptotic solutions to the WDW equation near the singularity are found, which reduce the problem to the so-called quantum billiard on the (n-1)-dimensional Lobachevsky space H^{n-1}. Two examples of quantum billiards are considered: a 2-dimensional quantum billiard for a 4D model with three 2-forms and a 9D quantum billiard for an 11D model with 120 4-forms which mimics SM2-brane sector of D=11 supergravity. For certain solutions, vanishing of the wave function at the singularity is proved.
Cite
@article{arxiv.1306.6521,
title = {Quantum billiards in multidimensional models with fields of forms},
author = {V. D. Ivashchuk and V. N. Melnikov},
journal= {arXiv preprint arXiv:1306.6521},
year = {2015}
}
Comments
14 pages, LaTex, no figures, several typos are eliminated