The commutative limit of a matrix geometry

Abstract

The noncommutative geometry of complex n×n matrices is considered as an approximation to the geometry of the two-sphere S2 and the differential forms defined over the matrices are mapped into the ordinary differential forms on SU2 considered as a fiber bundle over S2. It is found that the extra gauge-invariant vacuum studied in previous publications has as image a constant multiple of the connection on SU2 that defines the fibration, the Dirac monopole with unit magnetic charge.