Kinks and domain walls: an introduction to classical and quantum solitons

Tanmay Vachaspati0521836050, 9780521836050, 9780511246579

Kinks and domain walls are the simplest kind of solitons and are invaluable for testing various ideas and for learning about non-perturbative aspects of field theories. They are the subject of research in essentially every branch of physics, ranging from condensed matter to cosmology. This 2006 book is an introduction to kinks and domain walls and their principal classical and quantum properties. The book examines classical solitons, building from examples in elementary systems to more complicated settings. The formation of solitons in phase transitions, their dynamics and their cosmological consequences are further discussed. The book closes with an explicit description of a few laboratory systems containing solitons. Kinks and Domain Walls includes several state-of-the-art results, some previously unpublished. Each chapter closes with open questions and research problems and will be of great interest to both graduate students and academic researchers in theoretical physics, particle physics, cosmology and condensed matter physics.

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Table of contents :
Cover……Page 1
Half-title……Page 3
Title……Page 5
Copyright……Page 6
Dedication……Page 7
Contents……Page 9
Preface……Page 13
1 Classical kinks……Page 17
1.1 Z kink……Page 18
1.3 Derrick’s argument……Page 22
1.5 Bogomolnyi method for Z kink……Page 23
1.6 Z antikink……Page 24
1.7 Many kinks……Page 25
1.8 Inter-kink force……Page 26
1.9 Sine-Gordon kink……Page 28
1.10 Topology: Pi……Page 30
1.11 Bogomolnyi method revisited……Page 33
1.12 On more techniques……Page 34
1.13 Open questions……Page 35
2 Kinks in more complicated models……Page 36
2.1 SU(5) model……Page 37
2.2 SU(5) × Z symmetry breaking and topological kinks……Page 38
2.3 Non-topological SU(5) × Z kinks……Page 42
2.4 Space of SU(5) × Z kinks……Page 43
2.5 S kinks……Page 44
2.6 Symmetries within kinks……Page 45
2.7 Interactions of static kinks in non-Abelian models……Page 47
2.8 Kink lattices……Page 48
2.9 Open questions……Page 50
3.1 Breathers and oscillons……Page 51
3.2 Kinks and radiation……Page 54
3.3 Structure of the fluctuation Hamiltonian……Page 55
3.4 Interaction of kinks and radiation……Page 56
3.5 Radiation from kink deformations……Page 58
3.7 Scattering of kinks……Page 61
3.9 Open questions……Page 64
4 Kinks in quantum field theory……Page 66
4.1 Quantization of kinks: broad outline……Page 67
4.2 Example: Z kink……Page 74
4.3 Example: sine-Gordon kink……Page 76
4.4 Quantized excitations of the kink……Page 78
4.5 Sign of the leading order correction……Page 79
4.6 Boson-fermion connection……Page 81
4.7 Equivalence of sine-Gordon and massive Thirring models……Page 83
4.9 Comments……Page 86
4.10 Open questions……Page 87
5 Condensates and zero modes on kinks……Page 89
5.1 Bosonic condensates……Page 90
5.1.1 Bosonic condensate: an example……Page 91
5.2 Fermionic zero modes……Page 92
5.3 Fractional quantum numbers……Page 97
5.4 Other consequences……Page 98
5.5 Condensates on SU(5) × Z kinks……Page 100
5.6 Possibility of fermion bound states……Page 104
5.7 Open questions……Page 105
6.1 Effective potential……Page 106
6.2 Phase dynamics……Page 109
6.3 Kibble mechanism: first-order phase transition……Page 111
6.4 Correlation length……Page 113
6.5 Kibble-Zurek mechanism: second-order phase transition……Page 117
6.6.1 Z network……Page 121
6.6.2 SU(5) network……Page 122
6.7 Formation of S × Z domain wall network……Page 123
6.8 Biased phase transitions……Page 126
6.9 Open questions……Page 128
7.1 Kinks in 1 + 1 dimensions……Page 129
7.2 Walls in 3 + 1 dimensions……Page 132
7.3 Some solutions……Page 134
7.3.1 Planar solutions: traveling waves……Page 135
7.3.2 Axially symmetric walls……Page 136
7.3.3 Spherical walls……Page 138
7.4 Solutions in field theory: traveling waves……Page 141
7.6 Kink lattice dynamics (Toda lattice)……Page 142
7.7 Open questions……Page 143
8.1 Energy-momentum of domain walls……Page 144
8.2 Gravity: thin planar domain walls……Page 145
8.3 Gravitational properties of the thin planar wall……Page 146
8.4 Gravity: thick planar wall……Page 148
8.5 Topological inflation……Page 149
8.6 Spherical domain wall……Page 150
8.7 Scalar and gravitational radiation from domain walls……Page 151
8.9 Cosmological domain walls: formation……Page 152
8.10 Cosmological domain walls: evolution……Page 153
8.12 Evolution: analytical work……Page 155
8.13 Cosmological constraints……Page 157
8.14 Constraints on and implications for particle physics……Page 158
8.15 Metastable domain walls……Page 159
8.16 Open questions……Page 162
9.1 Polyacetylene……Page 163
9.2 Josephson junction transmission line……Page 165
9.4 Concluding remarks……Page 168
9.5 Open questions……Page 169
Appendix A Units, numbers and conventions……Page 170
Appendix B SU(N) generators……Page 171
Appendix C Solution to a common differential equation……Page 173
Identity 1……Page 175
Identity 3……Page 176
Appendix E Variation of the determinant……Page 178
Appendix F Summary of cosmological equations……Page 179
References……Page 181
Index……Page 190