Magnetic translation groups in an n-dimensional torus and their representations

DOI10.1063/1.1513208zbMath1060.81528arXivhep-th/0205053OpenAlexW1759988987MaRDI QIDQ4832833

Shogo Tanimura

Publication date: 14 December 2004

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/0205053

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70) Applications of group representations to physics and other areas of science (20C35)

Related Items (4)

On quantum mechanics with a magnetic field on \(\mathbb R^n\) and on a torus \(\mathbb T^n\), and their relation ⋮ An extension of Fourier analysis for the n-torus in the magnetic field and its application to spectral analysis of the magnetic Laplacian ⋮ QUANTIZATION ON A TORUS WITHOUT POSITION OPERATORS ⋮ Landau problem with a general time-dependent electric field

Cites Work

• The hierarchy problem and new dimensions at a millimeter
• Schrödinger operators with magnetic fields. III: Atoms in homogeneous magnetic field
• Schrödinger operators with magnetic fields. I: General interactions
• Separation of center of mass in homogeneous magnetic fields
• Magnetic Bloch analysis and Bochner Laplacians
• MacLane method of group cohomologies and gauge theories on finite lattices
• Magnetic translation groups as group extensions
• Magnetic translation groups on a \(3\times 3\)-torus. Application of the Mac Lane method
• The magnetic translation group in case \(N=2\)
• Magnetic translation groups in \(n\) dimensions
• Mac Lane method in the investigation of magnetic translation groups
• Bloch theory and quantization of magnetic systems
• Physical instances of noncommuting coordinates
• Stability of gaps for periodic potentials under variation of a magnetic field
• Novel phase structure of twisted \(\text{O}(N)\) \(\phi^ 4\) model on \(M^{D-1}\otimes S^ 1\).
• Spontaneous breaking of the rotational symmetry induced by monopoles in extra dimensions

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