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29 March 2024
 
  » arxiv » hep-th/9406013

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The Chern-Simons Action in Non-Commutative Geometry
A. H. Chamseddine ; J. Fröhlich ;
Date 3 Jun 1994
Journal J.Math.Phys. 35 (1994) 5195-5218
Subject High Energy Physics - Theory; Quantum Algebra | hep-th math.QA
AbstractA 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.
Source arXiv, hep-th/9406013
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