The Chern-Simons Action in Non-Commutative Geometry

Details The Chern-Simons Action in Non-Commutative Geometry The Chern-Simons Action in Non-Commutative Geometry

1994-06-03

arxiv.org/abs/hep-th/9406013v1

J.Math.Phys. 35 (1994) 5195-5218

Physics

High Energy Physics

High Energy Physics - Theory

40 pages

Scientific paper

10.1063/1.530748

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.

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