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Quantum billiards in multidimensional models with fields of forms

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Abstract

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.

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Authors and Affiliations

  1. Center for Gravitation and Fundamental Metrology, VNIIMS, Ozyornaya 46, Moscow, 119361, Russia

    V. D. Ivashchuk & V. N. Melnikov

  2. Institute of Gravitation and Cosmology of Peoples’ Friendship University of Russia, ul. Miklukho-Maklaya 6, Moscow, 117198, Russia

    V. D. Ivashchuk & V. N. Melnikov

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  1. V. D. Ivashchuk
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  2. V. N. Melnikov
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Correspondence to V. D. Ivashchuk.

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Ivashchuk, V.D., Melnikov, V.N. Quantum billiards in multidimensional models with fields of forms. Gravit. Cosmol. 19, 171–177 (2013). https://doi.org/10.1134/S0202289313030055

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