Abstract: Originated from the theory of connections on vector bundles over the spin manifolds, inner fluctuations of Dirac operator of spectral triples provide a mechanism through which the gauge fields can be implemented in the noncommutative geometry. In this talk, we shall go over the motivations and constructions that show why inner fluctuations can be interpreted as the gauge fields in the theory of spectral triples and how they generalize the gauge theory for the noncommutative geometries.

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