Quantum billiards in multidimensional models with branes

A gravitational D-dimensional model with l scalar fields and several forms is considered. When a cosmological-type diagonal metric 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 WDW equation are found in the limit of the formation of the billiard walls which reduce the problem to the so-called quantum billiard on the (Formula presented.)-dimensional Lobachevsky space. Two examples of quantum billiards are considered. The first one deals with (Formula presented.)-dimensional quantum billiard for (Formula presented.) model with (Formula presented.) four-forms which mimic space-like (Formula presented.)- and (Formula presented.)-branes of (Formula presented.) supergravity. The second one deals with the (Formula presented.)-dimensional quantum billiard for (Formula presented.) gravitational model with one scalar field, (Formula presented.) four-forms and (Formula presented.) three-forms which mimic space-like (Formula presented.)-, (Formula presented.)-, (Formula presented.)- and (Formula presented.)-branes in (Formula presented.) supergravity. It is shown that in both examples wave functions vanish in the limit of the formation of the billiard walls (i.e. we get a quantum resolution of the singularity for (Formula presented.) model) but magnetic branes could not be neglected in calculations of quantum asymptotic solutions while they are irrelevant for classical oscillating behavior when all (Formula presented.) electric branes are present. © 2014, The Author(s).