Billiard representation for multidimensional quantum cosmology near the singularity [chapter]

V. D. Ivashchuk, V. N. Melnikov
Birth of the Universe and Fundamental Physics  
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.
doi:10.1007/3-540-60024-8_87 fatcat:zjzrj4j66bb6nmwl3d5zrf7npe