%0 Journal Article
%T The Chern-Simons Action in Non-Commutative Geometry
%A A. H. Chamseddine
%A J. Fr£¿hlich
%J Physics
%D 1994
%I arXiv
%R 10.1063/1.530748
%X A general definition of Chern-Simons actions in non-commutative geometry is proposed and illustrated in several examples. These are based on ``space-times'' which are products of even-dimensional, Riemannian spin manifolds by a discrete (two-point) set. If the *algebras of operators describing the non-commutative spaces are generated by functions over such ``space-times'' with values in certain Clifford algebras the Chern-Simons actions turn out to be the actions of topological gravity on the even-dimensional spin manifolds. By contrasting the space of field configurations in these examples in an appropriate manner one is able to extract dynamical actions from Chern-Simons actions.
%U http://arxiv.org/abs/hep-th/9406013v1