Topological Solitons

TOPOLOGICAL SOLITONS 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 that 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. Nicholas Manton received his Ph.D. from the University of Cambridge in 1978. Following postdoctoral positions at the Ecole Normale Sup´er`ıeure in Paris; Massachusetts Institute of Technology; and University of California, Santa Barbara, he returned to Cambridge and is now Professor of Mathematical Physics in the Department of Applied Mathematics and Theoretical Physics. He is also head of the department’s High Energy Physics group, and 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. He also discovered, with Frans Klinkhamer, the unstable sphaleron solution in the electroweak theory of elementary particles. professor Manton was awarded the London Mathematical Society’s Whitehead Prize in 1991, and he was elected a fellow of the Royal Society in 1996. Paul Sutcliffe received his Ph.D. 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 has been 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. One of his principal research contributions was revealing the symmetric structures formed by Skyrmions and monopoles, their links with fullerenes in carbon chemistry, and finding associated novel scattering processes. He also discovered, with Richard Battye, the first stable knotted soliton solution in classical field theory. CAMBRIDGE MONOGRAPHS ON MATHEMATICAL PHYSICS General editors: P. V. Landshoff, D. R. Nelson, S. Weinberg S. J. Aarseth Gravitational N-Body Simulations J. Ambjørn, B. Durhuus and T. Jonsson Quantum Geometry: A Statistical Field Theory Approach A. M. Anile Relativistic Fluids and Magneto-Fluids J. A. de Azc´ arrage and J. M. Izquierdo Lie Groups, Lie Algebras, Cohomology and Some Applications in Physics† O. Babelon, D. Bernard and M. Talon Introduction to Classical Integrable Systems V. Belinkski and E. Verdaguer Gravitational Solitons J. Bernstein Kinetic Theory in the Early Universe G. F. Bertsch and R. A. Broglia Oscillations in Finite Quantum Systems N. D. Birrell and P. C. W. Davies Quantum Fields in Curved Space† M. Burgess Classical Covariant Fields S. Carlip Quantum Gravity in 2+1 Dimensions J. C. Collins Renormalization† M. Creutz Quarks, Gluons and Lattices† P. D. D’Earth Supersymmetric Quantum Cosmology F. de Felice and C. J. S Clarke Relativity on Curved Manifolds† P. G. O. Freund Introduction to Supersymmetry† J. Fuchs Affine Lie Algebras and Quantum Groups† J. Fuchs and C. Schweigert Symmetries, Lie Algebras and Representations: A Graduate Cou