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Selfdual Gauge Field Vortices

An Analytical Approach

Tarantello, Gabriella


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  • 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

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.

Content Level » Research

Keywords » Gauge theory - Partial differential equations - Quantum Hall effect - Theoretical physics - elliptic equations - mathematical physics - partial differential equation - quantum field theory

Related subjects » Birkhäuser Mathematics - Birkhäuser Physics

Table of contents 

Preface.- Selfdual Gauge Field Theories.- Elliptic Problems in the Study of Self-ual Vortex Configurations.- Planar Self-dual 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.- References.- Index.

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