Gauge theories in noncommutative geometry

Thierry Masson (1, 2, 3)

1 CPT - E2 Géométrie, Physique et Symétries
2 CPT - Centre de Physique Théorique - UMR 6207
3 CPT - Centre de Physique Théorique - UMR 7332

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.

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Thierry Masson. Gauge theories in noncommutative geometry. Joseph Kouneiher Cécile Barbachoux Thierry Masson and Dimitry Vey. Frontiers of Fundamental Physics: The Eleventh International Symposium, AIP, pp.73, 2012, AIP Conference Proceedings. ⟨hal-00963724⟩