Canonical commutation relations, the Weierstrass Zeta function, and infinite dimensional Hilbert space representations of the quantum group U q(𝔰𝔩2)

DOI10.1063/1.531797zbMath0897.47054OpenAlexW2155825005MaRDI QIDQ5284855

Asao Arai

Publication date: 2 April 1997

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

Full work available at URL: https://doi.org/10.1063/1.531797

zbMATH Keywords

quantum groupscanonical commutation relationsAharonov-Bohm effectWeierstrass zeta function

Mathematics Subject Classification ID

Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Applications of operator theory in the physical sciences (47N50) Commutation relations and statistics as related to quantum mechanics (general) (81S05)

Related Items (4)

Representation-theoretic aspects of two-dimensional quantum systems in singular vector potentials: Canonical commutation relations, quantum algebras, and reduction to lattice quantum systems ⋮ ZERO MODES IN A SYSTEM OF AHARONOV–BOHM FLUXES ⋮ A class of Hilbert space representations of the quantum plane and the quantum algebra \(U_q(\text{sl}_2)\) ⋮ PERIODIC AHARONOV–BOHM SOLENOIDS IN A CONSTANT MAGNETIC FIELD

Cites Work

• 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

This page was built for publication: Canonical commutation relations, the Weierstrass Zeta function, and infinite dimensional Hilbert space representations of the quantum group U q(𝔰𝔩2)