Bloch theory and quantization of magnetic systems

DOI10.1016/S0393-0440(99)00059-5zbMath1043.53067arXivmath-ph/9903048OpenAlexW1975389528MaRDI QIDQ1576290

Michael J. Gruber

Publication date: 2000

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/9903048

zbMATH Keywords

Schrödinger operatorGeometric quantizationSpectral theoryBochner LaplacianBloch theoryMagnetic fields

Mathematics Subject Classification ID

Geometry and quantization, symplectic methods (81S10) Applications of PDEs on manifolds (58J90) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70) Geometric quantization (53D50)

Related Items (8)

On quantum mechanics with a magnetic field on \(\mathbb R^n\) and on a torus \(\mathbb T^n\), and their relation ⋮ Magnetic translation groups in an n-dimensional torus and their representations ⋮ Analytic and algebraic properties of dispersion relations (Bloch varieties) and Fermi surfaces. What is known and unknown ⋮ Nonrelativistic hydrogen type stability problems on nonparabolic 3-manifolds ⋮ Noncommutative Bloch analysis of Bochner Laplacians with nonvanishing gauge fields ⋮ Generalized Bloch analysis and propagators on Riemannian manifolds with a discrete symmetry ⋮ Noncommutative Bloch theory ⋮ Smooth 2-group extensions and symmetries of bundle gerbes

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