Polynomial Heisenberg algebras and higher order supersymmetry

2000/11/01 by J C David Fernández, David J. Fernandez C., C., David J. Fernandez +3
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #hep-th #math-ph #math.MP #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/0011004

9 pages, latex, 3 postscript figures; talk given at the XXIII ICGTMP, Dubna (Russia) August 2000

arxiv created 2000/11/01 · openalex publication_date 2000/11/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

It is shown that the higher order supersymmetric partners of the harmonic oscillator Hamiltonian provide the simplest non-trivial realizations of the polynomial Heisenberg algebras. A linearized version of the corresponding annihilation and creation operator leads to a Fock representation which is the same as for the harmonic oscillator Hamiltonian

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