The Geometry and Dynamics of Magnetic Monopoles
The Geometry and Dynamics of Magnetic Monopoles
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DOI：
10.1515/9781400859306
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发表时间：
1988
期刊：
影响因子：
--
通讯作者：
M. Atiyah;N. Hitchin
中科院分区：
文献类型：
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作者：
M. Atiyah;N. Hitchin
由非线性微分方程控制的系统在所有科学分支中都具有根本的重要性，但我们对它们的理解仍然非常有限。在这本书中，一个特殊的系统，描述磁单极子的相互作用，详细研究。新的几何方法的使用产生了一个相当清晰的图片动态缓慢移动的单极子。这幅图阐明了近年来备受关注的孤子的重要概念。孤立子的想法桥梁之间的差距差距的概念“场”和“粒子“，并在这里探讨在一个完全三维的上下文中。虽然工作的背景和动机来自物理学，但介绍是数学的。这本书是跨学科的，解决了对基本粒子或广义相对论感兴趣的理论物理学家和从事分析或几何工作的数学家的关注。几何和物理之间的相互作用通过非线性偏微分方程现在是在一个非常令人兴奋的阶段，这本书是对这一活动的贡献。
Systems governed by non-linear differential equations are of fundamental importance in all branches of science, but our understanding of them is still extremely limited. In this book a particular system, describing the interaction of magnetic monopoles, is investigated in detail. The use of new geometrical methods produces a reasonably clear picture of the dynamics for slowly moving monopoles. This picture clarifies the important notion of solitons, which has attracted much attention in recent years. The soliton idea bridges the gap between the concepts of "fields" and "particles, " and is here explored in a fully three-dimensional context. While the background and motivation for the work comes from physics, the presentation is mathematical.This book is interdisciplinary and addresses concerns of theoretical physicists interested in elementary particles or general relativity and mathematicians working in analysis or geometry. The interaction between geometry and physics through non-linear partial differential equations is now at a very exciting stage, and the book is a contribution to this activity.