Details
| Original language | English |
|---|---|
| Pages (from-to) | 137-154 |
| Number of pages | 18 |
| Journal | Journal of geometry and physics |
| Volume | 34 |
| Issue number | 2 |
| Publication status | Published - Jun 2000 |
| Externally published | Yes |
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.
Keywords
- 02.30 (secondary), 02.40.Vh (primary), 03.65, 58F06, 58G25, 81Q10 (secondary), 81S10 (primary), Bloch theory, Bochner Laplacian, Geometric quantization, Magnetic fields, Quantum mechanics, Schrödinger operator, Spectral theory
ASJC Scopus subject areas
- Mathematics(all)
- Mathematical Physics
- Physics and Astronomy(all)
- General Physics and Astronomy
- Mathematics(all)
- Geometry and Topology
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In: Journal of geometry and physics, Vol. 34, No. 2, 06.2000, p. 137-154.
Research output: Contribution to journal › Article › Research › peer review
}
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 -