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The structure of the solution set for the Yang-Mills equations

Published online by Cambridge University Press:  24 October 2008

Judith M. Arms
Judith M. Arms
Affiliation:
University of Washington, Seattle
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Abstract

The solution set for the (sourceless) Yang-Mills equations on a spacetime with compact Cauchy surface is a smooth manifold (i.e. the equations are linearization stable) except at solutions that are symmetric. At such symmetric solutions, the structure is described by a homogeneous quadratic form. The degeneracy space for this form is tangent to a manifold of symmetric solutions. Symmetry breaking occurs for perturbations in the nondegenerate directions of the quadratic form. The terms ‘symmetry’ and ‘stability’ in the present work are compared to these terms as used elsewhere in the literature.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 90 , Issue 2 , September 1981 , pp. 361 - 372
Copyright
Copyright © Cambridge Philosophical Society 1981

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