Representation-theoretic aspects of two-dimensional quantum systems in singular vector potentials: Canonical commutation relations, quantum algebras, and reduction to lattice quantum systems

DOI10.1063/1.532631zbMath1007.46063OpenAlexW2026458626MaRDI QIDQ4260493

Asao Arai

Publication date: 15 December 2002

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

Full work available at URL: http://hdl.handle.net/2115/13682

zbMATH Keywords

quantum groupcanonical commutation relationsselfadjoint operatorAharonov-Bohm effectparticleessentially selfadjointquantum planechargetwo-dimensional quantum systemsmagnetic translationsSchrödinger representation of CCRsingular vector potentials

Mathematics Subject Classification ID

Linear symmetric and selfadjoint operators (unbounded) (47B25) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Applications of functional analysis in quantum physics (46N50) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Other ``noncommutative mathematics based on (C^*)-algebra theory (46L89)

Related Items (8)

Hilbert space representations of generalized canonical commutation relations ⋮ An extension of Fourier analysis for the n-torus in the magnetic field and its application to spectral analysis of the magnetic Laplacian ⋮ Ultra-weak time operators of Schrödinger operators ⋮ GENERALIZED WEAK WEYL RELATION AND DECAY OF QUANTUM DYNAMICS ⋮ ZERO MODES IN A SYSTEM OF AHARONOV–BOHM FLUXES ⋮ Spectral flows associated to flux tubes ⋮ A class of Hilbert space representations of the quantum plane and the quantum algebra \(U_q(\text{sl}_2)\) ⋮ Spectral flow of monopole insertion in topological insulators

Cites Work

• Magnetic translation groups as group extensions
• Magnetic translation groups in \(n\) dimensions
• Die Eindeutigkeit der Schrödingerschen Operatoren
• Analysis of a family of strongly commuting self-adjoint operators with applications to perturbed d'Alembertians and the external field problem in quantum field theory
• Quantum group and magnetic translations Bethe ansatz for the Asbel-Hofstadter problem
• Significance of Electromagnetic Potentials in the Quantum Theory
• Momentum operators with gauge potentials, local quantization of magnetic flux, and representation of canonical commutation relations
• Properties of the Dirac–Weyl operator with a strongly singular gauge potentiala)
• Gauge theory on a non-simply connected domain and representations of canonical commutation relations
• Representation of Canonical Commutation Relations in a Gauge Theory, the Aharonov-Bohm Effect, and the Dirac-Weyl Operator
• Models of the Hofstadter-type
• Canonical commutation relations, the Weierstrass Zeta function, and infinite dimensional Hilbert space representations of the quantum group U q(𝔰𝔩2)

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