Ebook: Selfdual Gauge Field Vortices: An Analytical Approach

In modern theoretical physics, gauge field theories are of great importance since they keep internal symmetries and account for phenomena such as spontaneous symmetry breaking, the quantum Hall effect, charge fractionalization, superconductivity and supergravity. This monograph discusses specific examples of gauge field theories that exhibit a selfdual structure.

The author builds a foundation for gauge theory and selfdual vortices by introducing the basic mathematical language of the subject and formulating examples ranging from the well-known abelian–Higgs and Yang–Mills models to the Chern–Simons–Higgs theories (in both the abelian and non-abelian settings). Thereafter, the electroweak theory and self-gravitating electroweak strings are also examined, followed by the study of the differential problems that have emerged from the analysis of selfdual vortex configurations; in this regard the author treats elliptic problems involving exponential non-linearities, also in relation to concentration-compactness principles and blow-up analysis.

Many open questions still remain in the field and are examined in this comprehensive work in connection with Liouville-type equations and systems. The goal of this text is to form an understanding of selfdual solutions arising in a variety of physical contexts. Selfdual Gauge Field Vortices: An Analytical Approach is ideal for graduate students and researchers interested in partial differential equations and mathematical physics.

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Elliptic problems arise in the study of significant questions concerning vortices in various selfdual field theories, e.g., Chern - Simons and Electroweak theories. Despite progress in these directions, many open questions still remain and are examined in this work in connection with Liouville-type equations and systems.Key topics unfold systematically beginning with the foundations of gauge theory and examples of selfdual vortices; chapters thereafter treat elliptic problems involving selfdual vortices, Ginzburg - Landau and Chern - Simons models, concentration-compactness principles, and Maxwell - Chern - Simons vortices.To date there is no comprehensive examination of the subject. The primary orientation of the text is partial differential equations, but the reader should have knowledge of some basic tools in field theory. For graduate students and researchers in PDEs and mathematical physics.