From Quantum Optics to Non-Commutative Geometry : A Non-Commutative Version of the Hopf Bundle, Veronese Mapping and Spin Representation

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dc.creatorFujii, Kazuyuki
dc.date2005-02-26
dc.date2005-04-20
dc.date.accessioned2026-07-07T06:12:14Z
dc.date.available2026-07-07T06:12:14Z
dc.descriptionIn this paper we construct a non-commutative version of the Hopf bundle by making use of Jaynes-Commings model and so-called Quantum Diagonalization Method. The bundle has a kind of Dirac strings. However, they appear in only states containing the ground one (${\cal F}\times \{\ket{0}\} \cup \{\ket{0}\}\times {\cal F} \subset {\cal F}\times {\cal F}$) and don't appear in remaining excited states. This means that classical singularities are not universal in the process of non-commutativization. Based on this construction we moreover give a non-commutative version of both the Veronese mapping which is the mapping from $\fukuso P^{1}$ to $\fukuso P^{n}$ with mapping degree $n$ and the spin representation of the group SU(2). We also present some challenging problems concerning how classical (beautiful) properties can be extended to the non-commutative case.
dc.descriptionLatex files, 28 pages. Minor changes (one page increased). To appear in the special issue of International Journal of Geometric Methods in Modern Physics
dc.identifierhttps://arxiv.org/abs/quant-ph/0502174
dc.identifierhttp://arxiv.org/abs/quant-ph/0502174
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/92726
dc.subjectQuantum Physics
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.titleFrom Quantum Optics to Non-Commutative Geometry : A Non-Commutative Version of the Hopf Bundle, Veronese Mapping and Spin Representation
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