Gauge invariance of the Chern-Simons action in noncommutative geometry

Details Gauge invariance of the Chern-Simons action in noncommutative geometry Gauge invariance of the Chern-Simons action in noncommutative geometry

1998-10-23

arxiv.org/abs/math-ph/9810015v1

Physics

Mathematical Physics

Latex, 14 pages, To appear in the Proceeeding of the ISI GUCCIA workshop "Quantum groups, noncommutative geometry and fundamen

Scientific paper

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.

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