In this paper we construct a non-commutative version of the Hopf bundle bymaking use of Jaynes-Commings model and so-called Quantum DiagonalizationMethod. The bundle has a kind of Dirac strings. However, they appear in onlystates containing the ground one (${\cal F}\times \{\ket{0}\} \cup\{\ket{0}\}\times {\cal F} \subset {\cal F}\times {\cal F}$) and don't appearin remaining excited states. This means that classical singularities are notuniversal in the process of non-commutativization. Based on this construction we moreover give a non-commutative version of boththe Veronese mapping which is the mapping from $\fukuso P^{1}$ to $\fukusoP^{n}$ 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.
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机译：在本文中，我们利用Jaynes-Commings模型和所谓的量子对角化方法构造了Hopf束的非交换形式。捆绑包有一种狄拉克弦。但是，它们仅出现在包含底数（$ {\ cal F} \ times \ {\ ket {0} \} \ cup \ {\ ket {0} \} \ times {\ cal F} \ subset {\ cal F} \ times {\ cal F} $），并且不会出现在剩余的激发态中。这意味着在非交换化过程中，经典奇点并非普遍。此外，基于此构造，我们还提供了Veronese映射的非交换版本，该映射是从$ \ fukuso P ^ {1} $到$ \ fukusoP ^ {n} $的映射度为$ n $的映射以及的自旋表示组SU（2）。我们还提出了一些有关如何将经典（美丽）性质扩展到非交换情形的挑战性问题。
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