Gauge theory on a non-simply connected domain and representations of canonical commutation relations

DOI10.1063/1.531051zbMath0879.46037OpenAlexW2163986625MaRDI QIDQ4873295

Asao Arai

Publication date: 19 January 1998

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

Full work available at URL: https://doi.org/10.1063/1.531051

zbMATH Keywords

Lie algebraWilson loopsgauge fieldgauge potentialparticles in a magnetic fieldphysical momentumSchrödinger particlesWeyl reformulation of the Heisenberg relations

Mathematics Subject Classification ID

Applications of functional analysis in quantum physics (46N50) Commutation relations and statistics as related to quantum mechanics (general) (81S05)

Related Items (5)

Canonical commutation relations, the Weierstrass Zeta function, and infinite dimensional Hilbert space representations of the quantum group U q(𝔰𝔩2) ⋮ 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 ⋮ Particles in singular magnetic field ⋮ Particles and quantum symmetries

Cites Work

• Die Eindeutigkeit der Schrödingerschen Operatoren
• Weitere Beiträge zum Infinitesimalkalkül der Matrizen
• Significance of Electromagnetic Potentials in the Quantum Theory
• A remark concerning canonical commutation relations
• 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)

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