Jaynes-Cummings model and a non-commutative geometry: A Few problems noted
Nov, 2004Citations per year
Abstract:
In 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 pa-
rameters 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 (F × {|0〉} ∪ {|0〉} × F), while for other excited states (F × F \ F × {|0〉} ∪ {|0〉} × 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 partlyNote:
- Latex files, 16 pages. Talk at "Yamagata Conference on Mathematical Sciences" (4~6/November/2004). An appendix added
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