Quantum billiards in multidimensional models with fields of forms

A 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 ℍn-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, whichmimics the SM2-brane sector of D = 11 supergravity. For certain solutions, vanishing of the wave function at the singularity is proved. © 2013 Pleiades Publishing, Ltd.

Authors
Number of issue
3
Language
English
Pages
171-177
Status
Published
Volume
19
Year
2013
Organizations
  • 1 Center for Gravitation and Fundamental Metrology, VNIIMS, Ozyornaya 46, Moscow, 119361, Russian Federation
  • 2 Institute of Gravitation and Cosmology of Peoples' Friendship University of Russia, ul. Miklukho-Maklaya 6, Moscow, 117198, Russian Federation
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/2048/
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