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Dirac operator on the quantum fuzzy four-sphere \(S_{q F}^4\). (English) Zbl 1456.81171

Summary: \(q\)-deformed fuzzy Dirac and chirality operators on quantum fuzzy four-sphere \(S_{q F}^4\) 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 \(q \rightarrow 1\) and the noncommutative parameter \(l\) tends to infinity.
©2021 American Institute of Physics

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81R20 Covariant wave equations in quantum theory, relativistic quantum mechanics
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
17B37 Quantum groups (quantized enveloping algebras) and related deformations
03E72 Theory of fuzzy sets, etc.
08A72 Fuzzy algebraic structures
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