arXiv 0907.29772009-07hep-thgr-qchep-lathep-phmath.QA

Fuzzy 2-球面上的自旋$j$ Dirac算子

Spin $j$ Dirac Operators on the Fuzzy 2-Sphere

A. P. Balachandran, Pramod Padmanabhan

备注：: 16 pages, 1 table
发表信息：: JHEP 0909:120,2009
DOI：: 10.1088/1126-6708/2009/09/120

摘要：

利用Ginsparg-Wilson（GW）代数[arxiv：hep-th/0511114]可以构造模糊2-球面$S^2_F$上的自旋1/2 Dirac算子及其手征性算子.这种构造实际上存在于$S^2_F$上的任何自旋$j$，并且在交换球$S^2$或$\mathbb{R}^{2}$上也有连续统类似物。这是一个值得注意的事实，在高维闵可夫斯基空间中没有已知的类似物。我们研究了$S^2_F$和交换$S^2$上的这类算子，并给出了从前者到后者极限存在的判据。这挑选出某些模糊版本的这些运营商作为首选狄拉克运营商。然后，我们研究了自旋1狄拉克算子的这种首选类型和它的手征上的模糊2-球，制定其瞬子部门和他们的指数理论。本文还详细研究了将这种分析推广到任意自旋$j$的方法。

英文摘要：

The spin 1/2 Dirac operator and its chirality operator on the fuzzy 2-sphere $S^2_F$ can be constructed using the Ginsparg-Wilson(GW) algebra [arxiv:hep-th/0511114]. This construction actually exists for any spin $j$ on $S^2_F$, and have continuum analogues as well on the commutative sphere $S^2$ or on $\mathbb{R}^{2}$. This is a remarkable fact and has no known analogue in higher dimensional Minkowski spaces. We study such operators on $S^2_F$ and the commutative $S^2$ and formulate criteria for the existence of the limit from the former to the latter. This singles out certain fuzzy versions of these operators as the preferred Dirac operators. We then study the spin 1 Dirac operator of this preferred type and its chirality on the fuzzy 2-sphere and formulate its instanton sectors and their index theory. The method to generalize this analysis to any spin $j$ is also studied in detail.

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摘要：

英文摘要：

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