On the Stability of Yang-Mills Bundles over $S^4$

Details On the Stability of Yang-Mills Bundles over $S^4$ On the Stability of Yang-Mills Bundles over $S^4$

2003-09-09

arxiv.org/abs/hep-th/0309090v2

Physics

High Energy Physics

High Energy Physics - Theory

17 pages

Scientific paper

The stability of Yang-Mills bundles over the usual $S^4$ space-time manifold is investigated according to the topological methods. The necessary gauge- and topological invaraint criterion for the exsitence of the related critical points is defined. It is shown that according to this criterion there exists no critical point even for the action functional of the standard U(1) gauge theory of electrodynamics on a $S^4$ manifold in view of its topological structure and therefore such a theory can not be stable. We will discuss also a general consequence of this result according to which for a stable U(1) Yang-Mills theory over a compact 4-manifold, this manifold should possess some self consistent compact 2-manifold substructure. These results are also in agreement with the known very general result for the {\it structural stability} of dynamical systems.

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