The Chern-Simons Action in Non-Commutative Geometry

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.

40 pages

References in corpus (2)

• Gravity in Non-Commutative Geometry
• Grand Unification in Non-Commutative Geometry

Cited by in corpus (14)

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• Computing noncommutative Chern-Simons theory radiative corrections on the back of an envelope
• Gauge fields on noncommutative geometries with curvature
• Noncommutative Fluids
• Finite Temperature effects on the Induced Chern-Simons term in noncommutative geometry
• Deformed "Commutative" Chern - Simons System
• Generalized Gauge Theories and Weinberg-Salam Model with Dirac-Kähler Fermions
• Induced QCD from the Noncommutative Geometry of a Supermanifold