1306.6521 (V. D. Ivashchuk et al.)

Quantum billiards in multidimensional models with fields of forms    [PDF]

V. D. Ivashchuk, V. N. Melnikov

Cosmological Bianchi-I type model in the (n+1)-dimensional gravitational theory with several forms is considered. When electric non-composite brane ansatz is adopted the Wheeler-DeWitt (WDW) equation for the model, written in the conformally-covariant form, is analyzed. Under certain restrictions asymptotic solutions to 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: 2-dimensional quantum billiard for 4-dimensional model with three 2-forms and 9-dimensional quantum billiard for D = 11 model with 120 4-forms which mimic M2-brane solutions of D=11 supergravity. For certain asymptotic solutions the vanishing of the wave function at the singularity is proved.

View original: http://arxiv.org/abs/1306.6521