Quantum billiards in multidimensional models with fields of forms on a product of Einstein spaces
- Авторлар: Ivashchuk V.1,2, Melnikov V.1,2
-
Мекемелер:
- Center for Gravitation and Fundamental Metrology
- Institute of Gravitation and Cosmology
- Шығарылым: Том 22, № 2 (2016)
- Беттер: 166-178
- Бөлім: Article
- URL: https://journals.rcsi.science/0202-2893/article/view/176022
- DOI: https://doi.org/10.1134/S0202289316020079
- ID: 176022
Дәйексөз келтіру
Аннотация
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.
Негізгі сөздер
Авторлар туралы
V. Ivashchuk
Center for Gravitation and Fundamental Metrology; Institute of Gravitation and Cosmology
Хат алмасуға жауапты Автор.
Email: ivashchuk@mail.ru
Ресей, ul. Ozernaya 46, Moscow, 119361; ul. Miklukho-Maklaya 6, Moscow, 117198
V. Melnikov
Center for Gravitation and Fundamental Metrology; Institute of Gravitation and Cosmology
Email: ivashchuk@mail.ru
Ресей, ul. Ozernaya 46, Moscow, 119361; ul. Miklukho-Maklaya 6, Moscow, 117198