On a Dirac particle in an uniform magnetic field in 3-dimensional spaces of constant curvature

Details On a Dirac particle in an uniform magnetic field in 3-dimensional spaces of constant curvature On a Dirac particle in an uniform magnetic field in 3-dimensional spaces of constant curvature

Publishing date

2010-07-24

URL

arxiv.org/abs/1007.4253v2

Science

Physics

Field

Mathematical Physics

Additional info

34 pages, Submitted to SIGMA

Type

Scientific paper

Abstract

There are constructed exact solutions of the quantum-mechanical Dirac equation for a spin S=1/2 particle in Riemannian space of constant negative curvature, hyperbolic Lobachevsky space, in presence of an external magnetic field, analogue of the homogeneous magnetic field in the Minkowski space. A generalized formula for energy levels, describing quantization of the transversal motion of the particle in magnetic field has been obtained. The same problem is solved for spin 1/2 particle in the space of constant positive curvature, spherical Riemann space. A generalized formula for energy levels, describing quantization of the transversal and along the magnetic field motions of the particle on the background of the Riemann space geometry, is obtained.

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