Abstract
This paper (Part I) and the sequel (Part II) prove the existence of a smooth, non-trivial, finite action solution to the SU (2) Yang-Mills-Higgs equations on ℝ3 in the Bogomol'nyi-Prasad-Sommerfield limit. The proof uses a simple form of Morse theory known as Ljusternik-Šnirelman theory. Part I establishes that a form of Lusternik-Šnirelman theory is applicable to the SU (2) Yang-Mills-Higgs equations. Here, a sufficient condition for the existence of the aforementioned solution is derived. Part II contains the completed existence proof. There it is demonstrated that the sufficient condition of Part I is satisfied by the SU (2) Yang-Mills-Higgs equations.
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Communicated by A. Jaffe
Research is supported in part by the Harvard Society of Fellows and the National Science Foundation under Grant PHY 79-16812
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Taubes, C.H. The existence of a non-minimal solution to the SU (2) Yang-Mills-Higgs equations on ℝ3. Part I. Commun.Math. Phys. 86, 257–298 (1982). https://doi.org/10.1007/BF01206014
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DOI: https://doi.org/10.1007/BF01206014