Geometric quantization of a particle in a perpendicular magnetic field. (English) Zbl 1373.53123

The authors of this paper study the quantization of a particle in the plane under the influence of a perpendicular magnetic field, using geometric quantization and half-forms in the Hilbert space of holomorphic functions. Relying on a judiciously chosen coordinate transformation they are able to convert the problem into a system of harmonic oscillators. The later problem is solved directly and, as a bonus, the relationship between different representations is highlighted as well. Finally, the authors point out the isomorphism between the holomorphic representation and the standard Schrödinger representation.


53D50 Geometric quantization
81S10 Geometry and quantization, symplectic methods
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