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

Capobianco, Guillermo; Reartes, Walter

J. Geom. Symmetry Phys. 41, 17-32 (2016).

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.

Reviewer: Ivailo Mladenov (Sofia)

MSC:

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

Keywords:

geometric quantization; Landau levels; Segal-Bargmann transform