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The Local Index Formula in Noncommutative Geometry

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Noncommutative Geometry and Particle Physics

Part of the book series: Mathematical Physics Studies ((MPST))

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Abstract

In this chapter we present a proof of the Connes–Moscovici index formula, expressing the index of a (twisted) operator \(D\) in a spectral triple \((\mathcal {A},\mathcal {H},D)\) by a local formula. First, we illustrate the contents of this chapter in the context of two examples in the odd and even case: the index on the circle and on the torus.

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Authors and Affiliations

  1. IMAPP, Radboud University Nijmegen, Nijmegen, The Netherlands

    Walter D. van Suijlekom

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  1. Walter D. van Suijlekom
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Correspondence to Walter D. van Suijlekom .

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van Suijlekom, W.D. (2015). The Local Index Formula in Noncommutative Geometry. In: Noncommutative Geometry and Particle Physics. Mathematical Physics Studies. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9162-5_5

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