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Anyons, Monopole and Coulomb Problem

A. Nersessian·V. M. Ter-Antonyan
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Abstract

The monopole systems with hidden symmetry of the two-dimensional Coulomb problem are considered. One of them, the "charge-charged magnetic vortex" with a half-spin, is constructed by reducing the quantum circular oscillator with respect to the action of the parity operator. The other two systems are constructed by reduction from the two-dimensional complex space. The first system is a particle on the sphere in the presence of the exterior constant magnetic field (generated by Dirac's monopole located in its center). This system is dual to the massless (3+1)-dimensional particle with fixed energy. The second system represents the particle on the pseudosphere in the presence of exterior magnetic field and is dual to the massive relativistic anyon.

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A. Nersessian, V. M. Ter-Antonyan. 1997-12-16. Anyons, Monopole and Coulomb Problem. https://arxiv.org/abs/physics/9712027

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