2005/02/26 by Kazuyuki Fujii, Fujii, Kazuyuki
Computer Science · Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Quantum Information and Cryptography #Quantum Physics (quant-ph) #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0502174
Latex files, 28 pages. Minor changes (one page increased). To appear in the special issue of International Journal of Geometric Methods in Modern Physics
openalex publication_date 2005/02/26 · arxiv created 2005/04/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 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× \\ket0\ ∪ \\ket0\× \cal F ⊂ \cal F× \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 P1 to \fukuso Pn 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.