Selfdual Gauge Field Vortices
An Analytical Approach
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Beschreibung
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.
This monograph discusses specific examples of selfdual gauge field structures. 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.
Provides foundation for gauge theory and selfdual vortices Advanced chapters treat elliptic problems involving Chern–Simmons models, concentration-compactness principles, and Maxwell–Chern–Simons vortices Examines Electroweak theory and self-gravitating Electroweak strings Discusses open questions in the field
Autor*in
Gabriella Tarantello
Themen in »Selfdual Gauge Field Vortices«
Gauge theory Partial differential equations Quantum Hall effect Theoretical physics elliptic equations mathematical physics partial differential equation quantum field theory
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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)()