The noncommutative geometry of Yang-Mills fields

作者：Boeijink Jord; van Suijlekom Walter D^*

来源：Journal of Geometry and Physics, 2011, 61(6): 1122-1134.

DOI：10.1016/j.geomphys.2011.02.010

• Noncommutative geometry
• Yang-Mills gauge theory

We generalize to topologically non-trivial gauge configurations the description of the Einstein-Yang-Mills system in terms of a noncommutative manifold, as was done previously by Chamseddine and Connes. Starting with an algebra bundle and a connection thereon, we obtain a spectral triple, a construction that can be related to the internal Kasparov product in unbounded KK-theory. In the case that the algebra bundle has typical fiber M(N) (C), we construct a PSU(N)-principal bundle for which it is an associated bundle. The so-called internal fluctuations of the spectral triple are parametrized by connections on this principal bundle and the spectral action gives the Yang-Mills action for these gauge fields, minimally coupled to gravity. Finally, we formulate a definition for a topological spectral action.

• 出版日期2011-6