The noncommutative geometry of Yang-Mills fields

Details The noncommutative geometry of Yang-Mills fields The noncommutative geometry of Yang-Mills fields

2010-08-30

arxiv.org/abs/1008.5101v1

J.Geom.Phys.61:1122-1134,2011

Physics

Mathematical Physics

14 pages

Scientific paper

10.1016/j.geomphys.2011.02.010

We generalize to topologically non-trivial gauge configurations the description of the Einstein-Yang-Mills system in terms of a noncommutative manifold, as was done previously by Chamseddine and Connes. Starting with an algebra bundle and a connection thereon, we obtain a spectral triple, a construction that can be related to the internal Kasparov product in unbounded KK-theory. In the case that the algebra bundle is an endomorphism bundle, we construct a PSU(N)-principal bundle for which it is an associated bundle. The so-called internal fluctuations of the spectral triple are parametrized by connections on this principal bundle and the spectral action gives the Yang-Mills action for these gauge fields, minimally coupled to gravity. Finally, we formulate a definition for a topological spectral action.

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