Local realizations of \(q\)-oscillators in quantum mechanics

DOI10.1016/0375-9601(96)00309-XzbMath0972.81578arXivhep-th/9604145MaRDI QIDQ1967895

Mikhail V. Ioffe, Alexander A. Andrianov, Francesco Cannata, Jean-Pierre Dedonder

Publication date: 7 March 2000

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9604145

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50)

Related Items (7)

The universal cardinal ordering of fixed points ⋮ Quons, coherent states and intertwining operators ⋮ DEFORMED HARMONIC OSCILLATOR AND NONLINEAR COHERENT STATES: NONCOMMUTATIVE QUANTUM SPACE APPROACH ⋮ Representations of the deformed oscillator algebra for different choices of generators ⋮ Properties of the algebra of \(q\)-deformed commutators in indefinite-metric space ⋮ Unified (p, q; α, β, ν; γ) −deformed oscillator algebra: Irreducible representations and induced deformed harmonic oscillator ⋮ Abstract ladder operators and their applications

Cites Work

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• A \(q\)-analogue of \(U(\mathfrak{gl}(N+1))\), Hecke algebra, and the Yang-Baxter equation
• Construction of reflectionless potentials with infinite discrete spectrum
• Polynomial SUSY in quantum mechanics and second derivative Darboux transformations
• SECOND ORDER DERIVATIVE SUPERSYMMETRY, q DEFORMATIONS AND THE SCATTERING PROBLEM
• On q-analogues of the quantum harmonic oscillator and the quantum group SU(2)_q
• On a general framework for q-particles, paraparticles and q-paraparticles through deformations
• Invariance properties of the q-oscillator algebra: q-analogue of von Neumann's theorem

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