Solitons in Field Theory and Nonlinear Analysis
By: by Yisong Yang
Series: Springer Monographs in Mathematics; Springer monographs in mathematics
Publisher: Springer New York
Published: 2001
Place of publication: New York, NY
Language: eng
Format: [electronic resource] /
Number of pages: 553
ISBN-13: 9781441929198; 9781475765489
Subjects: Mathematics; Global analysis (Mathematics)
Description: This book is on soliton solutions of elliptical partial differential equations arising in quantum field theory, such as vortices, instantons, monopoles, dyons, and cosmic strings. The book presents in-depth description of the problems of current interest, forging a link between mathematical analysis and physics and seeking to stimulate further research in the area. Physically, it touches the major branches of field theory: classical mechanics, special relativity, Maxwell equations, superconductivity, Yang-Mills gauge theory, general relativity, and cosmology. Mathematically, it involves Riemannian geometry, Lie groups and Lie algebras, algebraic topology (characteristic classes and homotropy) and emphasizes modern nonlinear functional analysis. There are many interesting and challenging problems in the area of classical field theory, and while this area has long been of interest to algebraists, geometers, and topologists, it has gradually begun to attract the attention of more analysts. This book written for researchers and graduate students will appeal to high-energy and condensed-matter physicists, mathematicians, and mathematical scientists.
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Table of contents: title: Preface; title: Primer of Field Theory; title: Sigma Models; title: Multiple Instantons and Characteristic Classes; title: Generalized Abelian Higgs Equations; title: Chern-Simons Systems: Abelian Case; title: Chern-Simons Systems: Non-Abelian Case; title: Electroweak Vortices; title: Dyons; title: Ordinary Differential Equations; title: Strings in Cosmology; title: Vortices and Antivortices; title: Born-Infeld Solutions; title: References; title: Bibliography; title: Index.