Kinks and Domain Walls: An Introduction to Classical and Quantum Solitons

Cover page\nHalf-title page\nFull title page\nCopyright page\nDedication page\nContents\nPreface\n1 Classical kinks\n	1.1 Z2 kink\n	1.2 Rescaling\n	1.3 Derrick’s argument\n	1.4 Domain walls\n	1.5 Bogomolnyi method for Z2 kink\n	1.6 Z2 antikink\n	1.7 Many kinks\n	1.8 Inter-kink force\n	1.9 Sine-Gordon kink\n	1.10 Topology: π0\n	1.11 Bogomolnyi method revisited\n	1.12 On more techniques\n	1.13 Open questions\n2 Kinks in more complicated models\n	2.1 SU(5) model\n	2.2 SU(5) × Z2 symmetry breaking and topological kinks\n	2.3 Non-topological SU(5) × Z2 kinks\n	2.4 Space of SU(5) × Z2 kinks\n	2.5 Sn kinks\n	2.6 Symmetries within kinks\n	2.7 Interactions of static kinks in non-Abelian models\n	2.8 Kink lattices\n	2.9 Open questions\n3 Interactions\n	3.1 Breathers and oscillons\n	3.2 Kinks and radiation\n	3.3 Structure of the fluctuation Hamiltonian\n	3.4 Interaction of kinks and radiation\n	3.5 Radiation from kink deformations\n	3.6 Kinks from radiation\n	3.7 Scattering of kinks\n	3.8 Intercommuting of domain walls\n	3.9 Open questions\n4 Kinks in quantum field theory\n	4.1 Quantization of kinks: broad outline\n	4.2 Example: Z2 kink\n	4.3 Example: sine-Gordon kink\n	4.4 Quantized excitations of the kink\n	4.5 Sign of the leading order correction\n	4.6 Boson-fermion connection\n	4.7 Equivalence of sine-Gordon and massive Thirring models\n	4.8 Z2 kinks on the lattice\n	4.9 Comments\n	4.10 Open questions\n5 Condensates and zero modes on kinks\n	5.1 Bosonic condensates\n	5.2 Fermionic zero modes\n	5.3 Fractional quantum numbers\n	5.4 Other consequences\n	5.5 Condensates on SU(5) × Z2 kinks\n	5.6 Possibility of fermion bound states\n	5.7 Open questions\n6 Formation of kinks\n	6.1 Effective potential\n	6.2 Phase dynamics\n	6.3 Kibble mechanism: first-order phase transition\n	6.4 Correlation length\n	6.5 Kibble-Zurek mechanism: second-order phase transition\n	6.6 Domain wall network formation\n	6.7 Formation of S5 × Z2 domain wall network\n	6.8 Biased phase transitions\n	6.9 Open questions\n7 Dynamics of domain walls\n	7.1 Kinks in 1 + 1 dimensions\n	7.2 Walls in 3 + 1 dimensions\n	7.3 Some solutions\n	7.4 Solutions in field theory: traveling waves\n	7.5 Spherical domain walls: field theory\n	7.6 Kink lattice dynamics (Toda lattice)\n	7.7 Open questions\n8 Gravity and cosmology of domain walls\n	8.1 Energy-momentum of domain walls\n	8.2 Gravity: thin planar domain walls\n	8.3 Gravitational properties of the thin planar wall\n	8.4 Gravity: thick planar wall\n	8.5 Topological inflation\n	8.6 Spherical domain wall\n	8.7 Scalar and gravitational radiation from domain walls\n	8.8 Collapse into black holes\n	8.9 Cosmological domain walls: formation\n	8.10 Cosmological domain walls: evolution\n	8.11 Evolution: numerical results\n	8.12 Evolution: analytical work\n	8.13 Cosmological constraints\n	8.14 Constraints on and implications for particle physics\n	8.15 Metastable domain walls\n	8.16 Open questions\n9 Kinks in the laboratory\n	9.1 Polyacetylene\n	9.2 Josephson junction transmission line\n	9.3 Solitons in shallow water\n	9.4 Concluding remarks\n	9.5 Open questions\nAppendix A Units, numbers and conventions\nAppendix B SU(N) generators\nAppendix C Solution to a common differential equation\nAppendix D Useful operator identities\nAppendix E Variation of the determinant\nAppendix F Summary of cosmological equations\nReferences\nIndex\nПустая страница