Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-05-02
Phys.Lett. B542 (2002) 295-300
Physics
High Energy Physics
High Energy Physics - Theory
7 pages
Scientific paper
10.1016/S0370-2693(02)02379-1
We compare the non-commutative quantum mechanics (NCQM) on sphere and the discrete part of the spectrum of NCQM on pseudosphere (Lobachevsky plane, or $AdS_2$) in the presence of a constant magnetic field $B$ with planar NCQM. We show, that (pseudo)spherical NCQM has a ``critical point'', where the system becomes effectively one-dimensional, and two different ``phases'', which the phases of the planar system originate from, specified by the sign of the parameter $\kappa=1-B\theta$. The ``critical point'' of (pseudo)spherical NCQM corresponds to the $\kappa\to\infty $ point of conventional planar NCQM, and to the ``critical point'' $\kappa=0$ of the so-called ``exotic'' planar NCQM, with a symplectic coupling of the (commutative) magnetic field.
Bellucci Stefano
Nersessian Armen
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