Gauge theories in noncommutative geometry

Details Gauge theories in noncommutative geometry Gauge theories in noncommutative geometry

2012-01-16

arxiv.org/abs/1201.3345v1

Physics

Mathematical Physics

28 pages. Review article to appear in the proceedings of the 11th annual international meeting "Fundamental Frontiers of Physi

Scientific paper

In this review we present some of the fundamental mathematical structures which permit to define noncommutative gauge field theories. In particular, we emphasize the theory of noncommutative connections, with the notions of curvatures and gauge transformations. Two different approaches to noncommutative geometry are covered: the one based on derivations and the one based on spectral triples. Examples of noncommutative gauge field theories are given to illustrate the constructions and to display some of the common features.

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