Topological Solitons (Google eBook)

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Cambridge University Press, Jun 10, 2004 - Science
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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.
  

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Contents

1 Introduction
1
2 Lagrangians and fields
15
3 Topology in field theory
47
4 Solitons general theory
75
5 Kinks
109
6 Lumps and rational maps
131
7 Vortices
158
8 Monopoles
241
9 Skyrmions
349
10 Instantons
416
11 Saddle points sphalerons
441
References
467
Index
491
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About the author (2004)

Nicholas Manton received his PhD from the University of Cambridge in 1978. Following postdoctoral positions at the Ecole Normale in Paris, M.I.T. and UC Santa Barbara, he returned to Cambridge and is now Professor of Mathematical Physics in the Department of Applied Mathematics and Theoretical Physics, and currently head of the department's High Energy Physics group. He is a Fellow of St John's College. He introduced and helped develop the method of modelling topological soliton dynamics by geodesic motion on soliton moduli spaces.

Paul Sutcliffe received his PhD from the University of Durham in 1992. Following postdoctoral appointments at Heriot-Watt, Orsay and Cambridge, he moved to the University of Kent, where he is now Reader in Mathematical Physics. For the past five years, he was an EPSRC Advanced Fellow. He has researched widely on topological solitons, especially multi-soliton solutions and soliton dynamics, and has found surprising relations between different kinds of soliton.

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