Quantum Hall effect on S 3 , edge states and fuzzy S 3 / Z 2
Quantum Hall effect on S 3 , edge states and fuzzy S 3 / Z 2
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量子霍尔效应对S 3 、边缘态和模糊S 3 / Z 2
DOI：
10.1016/j.nuclphysb.2003.11.028
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
S. Randjbar
中科院分区：
文献类型：
--
作者：
V. Nair;S. Randjbar
在背景场与自旋联系成正比的情况下，分析了S {sup 3}上的朗道问题和量子霍尔效应.场的有效强度可以通过改变费米子所属表象的维数来调整。得到了在费米子数目较多的情况下，量子霍尔液滴边缘激发的有效作用量。我们发现，对于许多这些考虑因素来说，适当的空间是S{sup 2}xS{sup 2}，它所起的作用类似于CP{sup 3}相对维斯S{sup 4}的作用。给出了模糊S{sup 3}/Z{sub 2}上的函数代数用有限维矩阵表示的方法。
We analyze the Landau problem and quantum Hall effect on S{sup 3} taking a constant background field proportional to the spin connection on S{sup 3}. The effective strength of the field can be tuned by changing the dimension of the representation to which the fermions belong. The effective action for the edge excitations of a quantum Hall droplet in the limit of a large number of fermions is obtained. We find that the appropriate space for many of these considerations is S{sup 2}xS{sup 2}, which plays a role similar to that of CP{sup 3} vis-a-vis S{sup 4}. We also give a method of representing the algebra of functions on fuzzy S{sup 3}/Z{sub 2} in terms of finite-dimensional matrices.