SU(n)-Gauge Theories in Noncommutative Differential Geometry

Michel Dubois-Violette (1) , Thierry Masson (1)

1 LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]

We study the noncommutative differential geometry of the algebra of endomorphisms of any SU(n)-vector bundle. We show that ordinary connections on such SU(n)-vector bundle can be interpreted in a natural way as a noncommutative 1-form on this algebra for the differential calculus based on derivations. We interpret the Lie algebra of derivations of the algebra of endomorphisms as a Lie algebroid. Then we look at noncommutative connections as generalizations of these usual connections.

Domaines: Géométrie différentielle [math.DG]

Michel Dubois-Violette, Thierry Masson. SU(n)-Gauge Theories in Noncommutative Differential Geometry. Journal of Geometry and Physics, 1998, 25, pp.104-118. ⟨hal-00013523⟩