Billiard Representation for Multidimensional Quantum Cosmology near the Singularity
V. D. Ivashchuk, V. N. Melnikov
Abstract
The degenerate Lagrangian system describing a lot of cosmological models is considered. When certain restrictions on the parameters of the model are imposed, the dynamics of the model near the "singularity" is reduced to a billiard on the Lobachevsky space. The Wheeler-DeWitt equation in the asymptotical regime is solved and a third-quantized model is suggested.
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