The Geometry and Dynamics of Magnetic Monopoles :The Geometry and Dynamics of Magnetic Monopoles ( Princeton Legacy Library )

Publication subTitle :The Geometry and Dynamics of Magnetic Monopoles

Publication series :Princeton Legacy Library

Author: Atiyah Michael Francis;Hitchin Nigel;;  

Publisher: Princeton University Press‎

Publication year: 2014

E-ISBN: 9781400859306

P-ISBN(Paperback): 9780691084800

Subject: O411 Mathematical Methods of Physics

Keyword: 物理学,数学

Language: ENG

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Description

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.

Originally published in 1988.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions.

Chapter

Contents

1. The Monopole Equations

2. Geometry of the Monopole Spaces

3. Metric of Monopole Spaces

4. Hyperkähler Property of the Metric

5. The Twistor Description

6. Particles and Symmetric Products

7. The 2-Monopole Space

8. Spectral Radii and the Conformal Structure

9. The Anti-Self-Dual Einstein Equations

10. Some Inequalities

11. The Metric on M02

12. Detailed Properties of the Metric

13. Geodesics on M02

14. Particle Scattering

15. Comparisons with KdV Solitons

16. Background Material

Bibliography

Index

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