Quantum billiards in multidimensional models with fields of forms on a product of Einstein spaces

The gravitational D-dimensional model is considered, with l scalar fields, a cosmological constant and several forms. When a cosmological block-diagonal metric, defined on a product of an 1-dimensional interval and n oriented Einstein spaces, is chosen, an electromagnetic composite brane ansatz is adopted, and certain restrictions on the branes are imposed, the conformally covariant Wheeler–DeWitt (WDW) equation for the model is studied. Under certain restrictions, asymptotic solutions to the WDWequation are found in the limit of the formation of billiard walls which reduce the problem to the socalled quantum billiard on (n + l - 1)-dimensional hyperbolic space. Several examples of billiards in the model with {pmn} non-intersecting electric branes, e.g., corresponding to hyperbolic Kac–Moody algebras, are considered. In the classical case, any of these billiards describe a never-ending oscillating behavior of scale factors while approaching to the singularity, which is either spacelike or timelike. For n = 2 the model is completely integrable in the asymptotic regime in the clasical and quantum cases. © 2016, Pleiades Publishing, Ltd.

Авторы
Номер выпуска
2
Язык
Английский
Страницы
166-178
Статус
Опубликовано
Том
22
Год
2016
Организации
  • 1 Center for Gravitation and Fundamental Metrology, VNIIMS, ul. Ozernaya 46, Moscow, 119361, Russian Federation
  • 2 Institute of Gravitation and Cosmology, Peoples’ Friendship University of Russia, ul. Miklukho-Maklaya 6, Moscow, 117198, Russian Federation
Дата создания
19.10.2018
Дата изменения
19.10.2018
Постоянная ссылка
https://repository.rudn.ru/ru/records/article/record/3968/