Singular Minkowski and Euclidean solutions forSU(2) Yang-Mills theory

Summary

In this paper we examine a solution to theSU(2) Yang-Mills-Higgs system, which is a trivial mathematical extension of recently dicovered Schwarzschild-like solutions (Singleton D.,Phys. Rev. D,51 (1955) 5911). Physically, however, this new solution has drastically different properties from the Schwarzschild-like solutions. We also study a new classical solution for EuclideanSU(2) Yang-Mills theory. Again this new solution is a mathematically trivial extension of the Belavin-Polyakov-Schwartz-Tyupkin (BPST) (Belavin A. A.et al., Phys. Lett. B,59 (1975) 85) instanton, but is physically very different. Unlike the usual instanton solution, the present solution is singular on a sphere of arbitrary radius in Euclidean space. Both of these solutions are infinite-energy solutions, so their practical value is somewhat unclear. However, they may be useful in exploring some of the mathematical aspects of classical Yang-Mills theory.