The Chern-Simons Action in Non-Commutative Geometry
High Energy Physics - Theory
2009-10-28 v1 Quantum Algebra
Abstract
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.
Cite
@article{arxiv.hep-th/9406013,
title = {The Chern-Simons Action in Non-Commutative Geometry},
author = {A. H. Chamseddine and J. Fröhlich},
journal= {arXiv preprint arXiv:hep-th/9406013},
year = {2009}
}
Comments
40 pages