Jaynes-Cummings Model and a Non-Commutative "Geometry" : A Few Problems Noted

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dc.creatorFujii, Kazuyuki
dc.date2004-10-26
dc.date2004-11-11
dc.date.accessioned2026-07-07T06:11:21Z
dc.date.available2026-07-07T06:11:21Z
dc.descriptionIn this paper we point out that the Jaynes-Cummings model without taking a renonance conditon gives a non-commutative version of the simple spin model (including the parameters $x$, $y$ and $z$) treated by M. V. Berry. This model is different from usual non-commutative ones because the x-y coordinates are quantized, while the z coordinate is not. One of new and interesting points in our non-commutative model is that the strings corresponding to Dirac ones in the Berry model exist only in states containing the ground state (${\cal F}\times \{\ket{0}\} \cup \{\ket{0}\}\times {\cal F}$), while for other excited states (${\cal F}\times {\cal F} \setminus {\cal F}\times \{\ket{0}\} \cup \{\ket{0}\}\times {\cal F}$) they don't exist. It is probable that a non-commutative model makes singular objects (singular points or singular lines or etc) in the corresponding classical model mild or removes them partly.
dc.descriptionLatex files, 16 pages. Talk at "Yamagata Conference on Mathematical Sciences" (4~6/November/2004). An appendix added
dc.identifierhttps://arxiv.org/abs/quant-ph/0410201
dc.identifierhttp://arxiv.org/abs/quant-ph/0410201
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/92462
dc.subjectQuantum Physics
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.titleJaynes-Cummings Model and a Non-Commutative "Geometry" : A Few Problems Noted
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