Titlebook: Noncommutative Geometry and Particle Physics; Walter D. van Suijlekom Textbook 20151st edition Springer Science+Business Media Dordrecht 2

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The Local Index Formula in Noncommutative GeometryIn this chapter we present a proof of the Connes–Moscovici index formula, expressing the index of a (twisted) operator . in a spectral triple . 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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Spectral InvariantsIn the previous chapter we have identified the gauge group canonically associated to any spectral triple and have derived the generalized gauge fields that carry an action of that gauge group.

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The Noncommutative Geometry of ElectrodynamicsIn the previous chapters we have described the general framework for the description of gauge theories in terms of noncommutative manifolds.

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Phenomenology of the Noncommutative Standard Model>In Theorems . and ., we have derived the full Lagrangian for the Standard Model from the almost-commutative manifold ..