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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 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.
Many open questions still remain in the field and are examined in this 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 and thus is ideal for graduate students and researchers interested in partial differential equations and mathematical physics.
List of contents
Selfdual Gauge Field Theories.- Elliptic Problems in the Study of Selfdual Vortex Configurations.- Planar Selfdual Chern-Simons Vortices.- Periodic Selfdual Chern-Simons Vortices.- The Analysis of Liouville-Type Equations With Singular Sources.- Mean Field Equations of Liouville-Type.- Selfdual Electroweak Vortices and Strings.
Summary
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 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.
Many open questions still remain in the field and are examined in this 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 and thus is ideal for graduate students and researchers interested in partial differential equations and mathematical physics.
Additional text
From the reviews:
“This monograph is devoted to a mathematical study of selfdual gauge theories using critical point theory and some analytical and topological techniques. … The book ends with a substantial bibliography and a useful index. This monograph, dealing in a clear way with some ‘hot’ topics of theoretical physics and geometry, will be of interest both to mathematicians and physicists.” (Jean Mawhin, Zentralblatt MATH, Vol. 1177, 2010)
Report
From the reviews:
"This monograph is devoted to a mathematical study of selfdual gauge theories using critical point theory and some analytical and topological techniques. ... The book ends with a substantial bibliography and a useful index. This monograph, dealing in a clear way with some 'hot' topics of theoretical physics and geometry, will be of interest both to mathematicians and physicists." (Jean Mawhin, Zentralblatt MATH, Vol. 1177, 2010)
