Authors:
- 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
Part of the book series: Progress in Nonlinear Differential Equations and Their Applications (PNLDE, volume 72)
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Table of contents (7 chapters)
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Front Matter
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Back Matter
About this book
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.
Reviews
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)Authors and Affiliations
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Dipartimento di Matematica, Università di Roma “Tor Vergata”, Rome, Italy
Gabriella Tarantello
Bibliographic Information
Book Title: Selfdual Gauge Field Vortices
Book Subtitle: An Analytical Approach
Authors: Gabriella Tarantello
Series Title: Progress in Nonlinear Differential Equations and Their Applications
DOI: https://doi.org/10.1007/978-0-8176-4608-0
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Birkhäuser Boston 2008
Hardcover ISBN: 978-0-8176-4310-2Published: 01 May 2008
eBook ISBN: 978-0-8176-4608-0Published: 16 April 2008
Series ISSN: 1421-1750
Series E-ISSN: 2374-0280
Edition Number: 1
Number of Pages: XIV, 325
Topics: Physics, general, Partial Differential Equations, Quantum Physics, Theoretical, Mathematical and Computational Physics