THE FLUX OF NONCOMMUTATIVE U(1) INSTANTON THROUGH THE FUZZY SPHERES

From the ADHM construction on noncommutative vector space, we investigate different U(1) instanton solutions tied by partial isometry transformations. We recast these solutions under a form of vector fields in noncommutative vector space which makes possible the calculus of their fluxes through fuzzy spheres. For this end, we establish the noncommutative analog of Gauss theorem from which we show that the flux of the U(1) instantons through fuzzy spheres does not depend on the radius of these spheres and it is invariant under partial isometry transformations.