Topological SolitonsCambridge University Press, 2004/06/10 - 493 ページ 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. |
目次
| 1 | |
| 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 |
| 467 | |
| 491 | |
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多く使われている語句
action ansatz approximation associated asymptotic Bogomolny equation boundary calculate centre Chapter charge circle close complex components condition configuration consider constant construction coordinates corresponding curve defined depends derivative described determined dimensions direction discussed dynamics energy example existence expression fact field field configuration field equation field theory finite follows force function gauge transformation geodesic given gives global implies infinity instantons integral invariant kink known Lagrangian leading limit lumps magnetic manifold mass metric minimal modes moduli space monopoles motion Nahm Note obtained origin parameter particles Phys plane positive possible potential rational map reduced representation result rotation satisfying scalar field scattering separated Skyrme Skyrmions solitons solution spatial static structure symmetry tetrahedral theory topological unit vacuum vector vortex vortices zero