In this paper, we have computed the spectrum and the $q$-index of the super $q$-deformed Ginsparg–Wilson Dirac operator in the different cases (fuzzy, non-fuzzy, gauged, and non-gauged) on the superquantum fuzzy two-sphere $S_{q\mu }^{(2|2)}$. We also presented the appropriate spin structure that this operator acts on the superquantum (Dirac) spinor bundle. Finally, it was shown that in the non-quantum limit, when $q$ tends to 1, in each case, there is a correct commutative limit for the spectrum and the $q$-index.

中文翻译：

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超量子模糊二球体Sqμ(2|2)上超q变形狄拉克算子的谱和q指数

在本文中，我们计算了超 $q$ 变形Ginsparg-Wilson Dirac算子在不同情况下（模糊、非模糊、测量、和非计量）在超量子模糊二球体 $S_{q\mu }^{(2|2)}$ 上。我们还提出了该算子作用于超量子（狄拉克）旋量丛的适当自旋结构。最后表明，在非量子极限下，当 $q$ 趋于1时，在每种情况下，谱和 $q$ 指数都存在正确的交换极限。