q-deformed fuzzy Dirac and chirality operators on quantum fuzzy four-sphere $S_{qF}^4$ are studied in this article. Using the q-deformed fuzzy Ginsparg–Wilson algebra, the q-deformed fuzzy Dirac and chirality operators in an instanton and no-instanton sector are studied. In addition, gauged Dirac and chirality operators in both cases have also been constructed. It has been shown that in each step, our results have a correct commutative limit in the limit case when q → 1 and the noncommutative parameter l tends to infinity.

中文翻译：

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量子模糊四球面上的Dirac算子

量子模糊四球面上的q变形Fuzzy Dirac和手性算子 ${\mathrm{小号}}_{qF}^4$在本文中进行研究。使用q变形的模糊Ginsparg–Wilson代数，研究了瞬时和非瞬时扇区中q变形的模糊Dirac和手性算子。此外，在两种情况下，都已构造了规范的Dirac和手性算子。已经证明，在每个步骤中，当q →1且非交换参数l趋于无穷大时，在极限情况下，我们的结果具有正确的交换极限。