Topological Solitons

Comprehensive survey of static topological solitons and their dynamical interactions, for graduates and researchers.

Nicholas Manton (Author), Paul Sutcliffe (Author)

9780521040969, Cambridge University Press

Paperback / softback, published 8 October 2007

508 pages, 76 b/w illus. 7 tables
24.4 x 17 x 2.6 cm, 0.8 kg

'… a unique, up-to-date and authoritative resource for anyone who wants to learn about the latest developments in the field of topological solitons. Moreover, by clearly exhibiting the essential idea of any topic they discuss, the authors have succeeded in writing a book which should teach mathematicians much about physics and physicists much about mathematics. The book is accessible to graduate students in theoretical physics and mathematics and despite the absence of exercises, could be used a s a textbook for an advanced lecture course.' Nieuw Archief voor Wiskunde

Topological solitons occur in many nonlinear classical field theories. They are stable, particle-like objects, with finite mass and a smooth structure. Examples are monopoles and Skyrmions, Ginzburg-Landau vortices and sigma-model lumps, and Yang-Mills instantons. This book is a comprehensive survey of static topological solitons and their dynamical interactions. Particular emphasis is placed on the solitons which satisfy first-order Bogomolny equations. For these, the soliton dynamics can be investigated by finding the geodesics on the moduli space of static multi-soliton solutions. Remarkable scattering processes can be understood this way. The book starts with an introduction to classical field theory, and a survey of several mathematical techniques useful for understanding many types of topological soliton. Subsequent chapters explore key examples of solitons in one, two, three and four dimensions. The final chapter discusses the unstable sphaleron solutions which exist in several field theories.

Preface
1. Introduction
2. Lagrangians and fields
3. Topology in field theory
4. Solitons - general theory
5. Kinks
6. Lumps and rational maps
7. Vortices
8. Monopoles
9. Skyrmions
10. Instantons
11. Saddle points - sphalerons
References
Index.

Subject Areas: Particle & high-energy physics [PHP], Physics [PH], Topology [PBP]