Selfdual Gauge Field Vortices
Selfdual Gauge Field Vortices
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DOI：
10.1007/978-0-8176-4608-0
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
G. Tarantello
中科院分区：
文献类型：
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作者：
G. Tarantello
在现代理论物理学中，规范场理论非常重要，因为它们保持内部对称性，并解释了诸如自发对称性破缺、量子霍尔效应、电荷分馏、超导和超引力等现象。这本专著讨论了自对偶规范场结构的具体例子，包括陈-西蒙斯模型、阿贝尔-希格斯模型和杨-米尔斯规范场理论。作者通过介绍规范理论的基本数学语言和陈-西蒙斯-希格斯理论（在阿贝尔和非阿贝尔设置）的例子，建立了规范理论和自对偶涡的基础。此后，研究了电弱理论和自引力电弱弦。最后几章处理椭圆问题，涉及陈-西蒙斯模型，浓度紧原则，麦克斯韦-陈-西蒙斯涡。许多悬而未决的问题仍然存在于该领域，并在这项工作中与刘维尔型方程和系统进行了审查。本文的目标是形成一个理解的自对偶解决方案中产生的各种物理环境，因此是理想的研究生和研究人员感兴趣的偏微分方程和数学物理。
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.