This monograph discusses specific examples of selfdual gauge field structures, including the Chern-Simons model, the abelian-Higgs model, and Yang-Mills gauge field theory. The author builds a foundation for gauge theory and selfdual vortices by introducing the basic mathematical language of gauge theory and formulating examples of Chern-Simons-Higgs theories (in both abelian and non-abelian settings). Thereafter, the Electroweak theory and self-gravitating Electroweak strings are examined. The final chapters treat elliptic problems involving Chern-Simmons models, concentration-compactness principles, and Maxwell-Chern-Simons vortices.
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