| Автор | M A Olshanetsky |
| Автор | V -B K Rogov |
| Дата выпуска | 1994-07-07 |
| dc.description | We consider the quantum Lobachevsky space L<sub>q</sub><sup>3</sup>, which is defined as a subalgebra of the Hopf algebra A<sub>q</sub>(SL<sub>2</sub>(C)). The Iwasawa decomposition of A<sub>q</sub>(SL<sub>2</sub>(C)) introduced by Podles and Woronowicz allows us to consider the quantum analogue of the horospheric coordinates on L<sub>q</sub><sup>3</sup>. The action of the Casimir element, which belongs to the dual to A<sub>q</sub> quantum group U<sub>q</sub>(SL<sub>2</sub>(C)), on some subspace in L<sub>q</sub><sup>3</sup> in these coordinates leads to a second order difference operator on the infinite one-dimensional lattice. In the continuous limit q to 1 it is transformed into the Schrodinger Hamiltonian, which describes zero modes into the Liouville field theory (the Liouville quantum mechanics). We calculate the spectrum (Brillouin zones) and the eigenfunctions of this operator. They are q-continuous Hermite polynomials, which are particular cases of the Macdonald or Rogers-Askey-Ismail polynomials. The scattering in this problem corresponds to the scattering of the first two-level dressed excitations in the Z<sub>N</sub> model in the very peculiar limit when the anisotropy parameter gamma and N to infinity , or, equivalently, ( gamma ,N) to 0. |
| Формат | application.pdf |
| Издатель | Institute of Physics Publishing |
| Название | Liouville quantum mechanics on a lattice from geometry of quantum Lorentz group |
| Тип | paper |
| DOI | 10.1088/0305-4470/27/13/040 |
| Print ISSN | 0305-4470 |
| Журнал | Journal of Physics A: Mathematical and General |
| Том | 27 |
| Первая страница | 4669 |
| Последняя страница | 4683 |
| Аффилиация | M A Olshanetsky; Inst. of Theor. & Exp. Phys., Moscow, Russia |
| Аффилиация | V -B K Rogov; Inst. of Theor. & Exp. Phys., Moscow, Russia |
| Выпуск | 13 |
