## Details

Originalsprache | Englisch |
---|---|

Seiten (von - bis) | 137-154 |

Seitenumfang | 18 |

Fachzeitschrift | Journal of geometry and physics |

Jahrgang | 34 |

Ausgabenummer | 2 |

Publikationsstatus | Veröffentlicht - Juni 2000 |

Extern publiziert | Ja |

## Abstract

Quantizing the motion of particles on a Riemannian manifold in the presence of a magnetic field poses the problems of existence and uniqueness of quantizations. Both of them are considered since the early days of geometric quantization but there is still some structural insight to gain from spectral theory. Following the work of Asch et al. (Magnetic Bloch analysis and Bochner Laplacians, J. Geom. Phys. 13 (3) (1994) 275-288) for the 2-torus we describe the relation between quantization on the manifold and Bloch theory on its covering space for more general compact manifolds.

## ASJC Scopus Sachgebiete

- Mathematik (insg.)
**Mathematische Physik****Physik und Astronomie (insg.)**- Mathematik (insg.)
**Geometrie und Topologie**

## Zitieren

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**Bloch theory and quantization of magnetic systems.**/ Gruber, Michael J.

in: Journal of geometry and physics, Jahrgang 34, Nr. 2, 06.2000, S. 137-154.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

*Journal of geometry and physics*, Jg. 34, Nr. 2, S. 137-154. https://doi.org/10.1016/S0393-0440(99)00059-5

}

TY - JOUR

T1 - Bloch theory and quantization of magnetic systems

AU - Gruber, Michael J.

N1 - Funding information: This work is a (commutative) part of my Ph.D. thesis “Nichtkommutative Blochtheorie” (non-commutative Bloch theory; [9] ). I gratefully appreciate the advice and supervision given by Jochen Brüning at Humboldt-University at Berlin. This work was supported by Deutsche Forschungsgemeinschaft as project D6 at the Sonderforschungsbereich 288 (differential geometry and quantum physics), where this article is available as preprint 375. Finally I would like to thank the referee for valuable remarks on the organisation of the paper and on some peculiarities of the quantization of quadratic Hamiltonians.

PY - 2000/6

Y1 - 2000/6

N2 - Quantizing the motion of particles on a Riemannian manifold in the presence of a magnetic field poses the problems of existence and uniqueness of quantizations. Both of them are considered since the early days of geometric quantization but there is still some structural insight to gain from spectral theory. Following the work of Asch et al. (Magnetic Bloch analysis and Bochner Laplacians, J. Geom. Phys. 13 (3) (1994) 275-288) for the 2-torus we describe the relation between quantization on the manifold and Bloch theory on its covering space for more general compact manifolds.

AB - Quantizing the motion of particles on a Riemannian manifold in the presence of a magnetic field poses the problems of existence and uniqueness of quantizations. Both of them are considered since the early days of geometric quantization but there is still some structural insight to gain from spectral theory. Following the work of Asch et al. (Magnetic Bloch analysis and Bochner Laplacians, J. Geom. Phys. 13 (3) (1994) 275-288) for the 2-torus we describe the relation between quantization on the manifold and Bloch theory on its covering space for more general compact manifolds.

KW - 02.30 (secondary)

KW - 02.40.Vh (primary)

KW - 03.65

KW - 58F06

KW - 58G25

KW - 81Q10 (secondary)

KW - 81S10 (primary)

KW - Bloch theory

KW - Bochner Laplacian

KW - Geometric quantization

KW - Magnetic fields

KW - Quantum mechanics

KW - Schrödinger operator

KW - Spectral theory

UR - http://www.scopus.com/inward/record.url?scp=0034196128&partnerID=8YFLogxK

U2 - 10.1016/S0393-0440(99)00059-5

DO - 10.1016/S0393-0440(99)00059-5

M3 - Article

AN - SCOPUS:0034196128

VL - 34

SP - 137

EP - 154

JO - Journal of geometry and physics

JF - Journal of geometry and physics

SN - 0393-0440

IS - 2

ER -