The spectral Dirac operator is a differential operator that arises in the context of noncommutative geometry, particularly in the study of spinors on noncommutative spaces. It plays a crucial role in defining the notion of a Dirac operator in a noncommutative framework, which generalizes the classical Dirac operator found in differential geometry. This operator captures important geometric and topological features of noncommutative spaces, allowing for the analysis of their spectral properties and connections to physical theories, such as quantum field theory.
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