1998/10/23 by T. Krajewski, Krajewski, T.
Mathematics · Physics and Astronomy · #81T13 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:81T13
paper · pdf · doi:10.48550/arxiv.math-ph/9810015
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
arxiv created 1998/10/23 · arxiv updated 2009/11/30
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.