Properties of the Dirac–Weyl operator with a strongly singular gauge potentiala)

DOI10.1063/1.530201zbMath0809.47057OpenAlexW1971507240MaRDI QIDQ4201760

Asao Arai

Publication date: 6 September 1993

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

Full work available at URL: https://doi.org/10.1063/1.530201

zbMATH Keywords

charged particlequantum systemperpendicular magnetic fieldtotal magnetic fluxzero-energy statesDirac-Weyl operatortwo- dimensional Dirac delta distributions

Mathematics Subject Classification ID

Applications of operator theory in the physical sciences (47N50) General theory of partial differential operators (47F05) Electromagnetic interaction; quantum electrodynamics (81V10)

Related Items (12)

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 ⋮ Scaling limit of anticommuting selfadjoint operators and applications to Dirac operators ⋮ Operator-theoretical analysis of a representation of a supersymmetry algebra in Hilbert space ⋮ On the Dirac and Pauli operators with several Aharonov-Bohm solenoids ⋮ Gauge theory on a non-simply connected domain and representations of canonical commutation relations ⋮ Geometric construction of \(*\)-representations of the Weyl algebra with degree 2 ⋮ ZERO MODES IN A SYSTEM OF AHARONOV–BOHM FLUXES ⋮ Ground state of a spin-1/2 charged particle in a two-dimensional magnetic field ⋮ Self-adjointness and spectral properties of Dirac operators with magnetic links ⋮ Strong anticommutativity of dirac operators on boson—fermion fock spaces and representations of a supersymmetry algebra ⋮ Characterization of anticommutativity of self-adjoint operators in connection with Clifford algebra and applications

Cites Work

• Dynamical breaking of supersymmetry
• Supersymmetry and singular perturbations
• Anticommuting selfadjoint operators
• A remark concerning canonical commutation relations
• On the degeneracy in the ground state of the N=2 Wess–Zumino supersymmetric quantum mechanics
• Witten index, axial anomaly, and Krein’s spectral shift function in supersymmetric quantum mechanics
• Existence of infinitely many zero-energy states in a model of supersymmetric quantum mechanics
• Momentum operators with gauge potentials, local quantization of magnetic flux, and representation of canonical commutation relations

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