LEADER 06084nam 22007212 450 001 9910457738703321 005 20151005020624.0 010 $a1-107-15061-2 010 $a1-280-54099-0 010 $a9786610540990 010 $a0-511-21499-5 010 $a0-511-21678-5 010 $a0-511-21141-4 010 $a0-511-33150-9 010 $a0-511-61703-8 010 $a0-511-21318-2 035 $a(CKB)1000000000352934 035 $a(EBL)266652 035 $a(OCoLC)171139050 035 $a(SSID)ssj0000260225 035 $a(PQKBManifestationID)11215937 035 $a(PQKBTitleCode)TC0000260225 035 $a(PQKBWorkID)10223843 035 $a(PQKB)11744423 035 $a(UkCbUP)CR9780511617034 035 $a(MiAaPQ)EBC266652 035 $a(Au-PeEL)EBL266652 035 $a(CaPaEBR)ebr10131629 035 $a(CaONFJC)MIL54099 035 $a(OCoLC)144618426 035 $a(EXLCZ)991000000000352934 100 $a20090915d2004|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aTopological solitons /$fNicholas Manton, Paul Sutcliffe$b[electronic resource] 210 1$aCambridge :$cCambridge University Press,$d2004. 215 $a1 online resource (xi, 493 pages) $cdigital, PDF file(s) 225 1 $aCambridge monographs on mathematical physics 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 311 $a0-521-04096-5 311 $a0-521-83836-3 320 $aIncludes bibliographical references (p. 467-490) and index. 327 $aCover; Half-title; Series-title; Title; Copyright; Contents; Preface; 1 Introduction; 1.1 Solitons as particles; 1.2 A brief history of topological solitons; 1.3 Bogomolny equations and moduli spaces; 1.4 Soliton dynamics; 1.5 Solitons and integrable systems; 1.6 Solitons - experimental status; 1.7 Outline of this book; 2 Lagrangians and fields; 2.1 Finite-dimensional systems; 2.2 Symmetries and conservation laws; 2.3 Field theory; 2.4 Noether's theorem in field theory; 2.5 Vacua and spontaneous symmetry breaking; 2.6 Gauge theory; 2.7 The Higgs mechanism; 2.8 Gradient flow in field theory 327 $a3 Topology in field theory3.1 Homotopy theory; 3.2 Topological degree; 3.3 Gauge fields as differential forms; 3.4 Chern numbers of abelian gauge .elds; 3.5 Chern numbers for non-abelian gauge fields; 3.6 Chern-Simons forms; 4 Solitons - general theory; 4.1 Topology and solitons; 4.2 Scaling arguments; 4.3 Symmetry and reduction of dimension; 4.4 Principle of symmetric criticality; 4.5 Moduli spaces and soliton dynamics; 5 Kinks; 5.1 Bogomolny bounds and vacuum structure; 5.2 Phi4 kinks; 5.3 Sine-Gordon kinks; 5.4 Generalizations; 6 Lumps and rational maps; 6.1 Lumps in the O(3) sigma model 327 $a6.2 Lumps on a sphere and symmetric maps6.3 Stabilizing the lump; 7 Vortices; 7.1 Ginzburg-Landau energy functions; 7.2 Topology in the global theory; 7.3 Topology in the gauged theory; 7.4 Vortex solutions; 7.5 Forces between gauged vortices; 7.6 Forces between vortices at large separation; 7.7 Dynamics of gauged vortices; 7.8 Vortices at critical coupling; 7.9 Moduli space dynamics; 7.10 The metric on MN; 7.11 Two-vortex scattering; 7.12 First order dynamics near critical coupling; 7.13 Global vortex dynamics; 7.14 Varying the geometry; 7.15 Statistical mechanics of vortices; 8 Monopoles 327 $a8.1 Dirac monopoles8.2 Monopoles as solitons; 8.3 Bogomolny-Prasad-Sommerfield monopoles; 8.4 Dyons; 8.5 The Nahm transform; 8.6 Construction of monopoles from Nahm data; 8.7 Spectral curves; 8.8 Rational maps and monopoles; 8.9 Alternative monopole methods; 8.10 Monopole dynamics; 8.11 Moduli spaces and geodesic motion; 8.12 Well separated monopoles; 8.13 SU(m) monopoles; 8.14 Hyperbolic monopoles; 9 Skyrmions; 9.1 The Skyrme model; 9.2 Hedgehogs; 9.3 Asymptotic interactions; 9.4 Low charge Skyrmions; 9.5 The rational map ansatz; 9.6 Higher charge Skyrmions; 9.7 Lattices, crystals and shells 327 $a9.8 Skyrmion dynamics9.9 Generalizations of the Skyrme model; 9.10 Quantization of Skyrmions; 9.11 The Skyrme-Faddeev model; 10 Instantons; 10.1 Self-dual Yang-Mills fields; 10.2 The ADHM construction; 10.3 Symmetric instantons; 10.4 Skyrme fields from instantons; 10.5 Monopoles as self-dual gauge fields; 10.6 Higher rank gauge groups; 11 Saddle points - sphalerons; 11.1 Mountain passes; 11.2 Sphalerons on a circle; 11.3 The gauged kink; 11.4 Monopole-antimonopole dipole; 11.5 The electroweak sphaleron; 11.6 Unstable solutions in other theories; References; Index 330 $aTopological solitons occur in many nonlinear classical field theories. They are stable, particle-like objects, with finite mass and a smooth structure. Examples are monopoles and Skyrmions, Ginzburg-Landau vortices and sigma-model lumps, and Yang-Mills instantons. This book is a comprehensive survey of static topological solitons and their dynamical interactions. Particular emphasis is placed on the solitons which satisfy first-order Bogomolny equations. For these, the soliton dynamics can be investigated by finding the geodesics on the moduli space of static multi-soliton solutions. Remarkable scattering processes can be understood this way. The book starts with an introduction to classical field theory, and a survey of several mathematical techniques useful for understanding many types of topological soliton. Subsequent chapters explore key examples of solitons in one, two, three and four dimensions. The final chapter discusses the unstable sphaleron solutions which exist in several field theories. 410 0$aCambridge monographs on mathematical physics. 606 $aSolitons 615 0$aSolitons. 676 $a530.14 700 $aManton$b Nicholas$f1952-$01042790 702 $aSutcliffe$b Paul$g(Paul M.), 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910457738703321 996 $aTopological solitons$92467298 997 $aUNINA