Solutions to YangMills Equations that are not SelfDual
Abstract
The YangMills functional for connections on principle SU(2) bundles over S^{4} is studied. Critical points of the functional satisfy a system of secondorder partial differential equations, the YangMills equations. If, in particular, the critical point is a minimum, it satisfies a firstorder system, the selfdual or antiselfdual equations. Here, we exhibit an infinite number of finiteaction nonminimal unstable critical points. They are obtained by constructing a topologically nontrivial loop of connections to which minmax theory is applied. The construction exploits the fundamental relationship between certain invariant instantons on S^{4} and magnetic monopoles on H^{3}. This result settles a question in gauge field theory that has been open for many years.
 Publication:

Proceedings of the National Academy of Science
 Pub Date:
 November 1989
 DOI:
 10.1073/pnas.86.22.8610
 Bibcode:
 1989PNAS...86.8610S