PROJECTORS FOR THE FUZZY SPHERE

Abstract

All fiber bundles with a given set of characteristic classes can be considered as particular projections of a more general bundle called a universal classifying space. This notion of projector valued field, a global definition of connections and gauge fields, may be useful in defining vector bundles for noncommutative base spaces. In this letter we derive the projector valued field for the fuzzy sphere, define noncommutative n-monopole configurations, and check that in the classical limit, using the machinery of noncommutative geometry, the corresponding topological charges (Chern class) are integers.