Quantum Harmonic Oscillator Algebra and Link Invariants

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dc.creatorGomez, C.
dc.creatorSierra, G.
dc.date1991-11-04
dc.date.accessioned2026-07-07T09:13:55Z
dc.date.available2026-07-07T09:13:55Z
dc.descriptionThe $q$--deformation $U_q (h_4)$ of the harmonic oscillator algebra is defined and proved to be a Ribbon Hopf algebra.Associated with this Hopf algebra we define an infinite dimensional braid group representation on the Hilbert space of the harmonic oscillator, and an extended Yang--Baxter system in the sense of Turaev. The corresponding link invariant is computed in some particular cases and coincides with the inverse of the Alexander--Conway polynomial. The $R$ matrix of $U_q (h_4)$ can be interpreted as defining a baxterization of the intertwiners for semicyclic representations of $SU(2)_q$ at $q=e^{2 πi/N}$ in the $N \rightarrow \infty$ limit.Finally we define new multicolored braid group representations and study their relation to the multivariable Alexander--Conway polynomial.
dc.description21 Pages
dc.identifierhttps://arxiv.org/abs/hep-th/9111005
dc.identifierhttp://arxiv.org/abs/hep-th/9111005
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/152493
dc.subjectHigh Energy Physics - Theory
dc.subjectQuantum Algebra
dc.titleQuantum Harmonic Oscillator Algebra and Link Invariants
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