Gauge invariance of the Chern-Simons action in noncommutative geometry
Abstract
Description
In complete analogy with the classical case, we define the Chern-Simons action functional in noncommutative geometry and study its properties under gauge transformations. As usual, the latter are related to the connectedness of the group of gauge transformations. We establish this result by making use of the coupling between cyclic cohomology and K-theory and prove, using an index theorem, that this coupling is quantized in the case of the noncommutative torus.
Latex, 14 pages, To appear in the Proceeeding of the ISI GUCCIA workshop "Quantum groups, noncommutative geometry and fundamental physical interactions", D. Kastler and M. Rosso editors
Latex, 14 pages, To appear in the Proceeeding of the ISI GUCCIA workshop "Quantum groups, noncommutative geometry and fundamental physical interactions", D. Kastler and M. Rosso editors