Phases in noncommutative quantum mechanics on (pseudo)sphere

Abstract

We compare the non-commutative quantum mechanics (NCQM) on sphere and the discrete part of the spectrum of NCQM on pseudosphere (Lobachevsky plane, or $Ad{S}_2$) 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.

7 pages

References in corpus (4)

• Spectrum of Schroedinger field in a noncommutative magnetic monopole
• Quantum mechanics on noncommutative Riemann surfaces
• Quantum mechanics on noncommutative plane and sphere from constrained systems
• Noncommutative quantum mechanics as a constrained system

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