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Tarantello G. — Self-Dual Gauge Field Vortices: An Analytical Approach
Tarantello G. — Self-Dual Gauge Field Vortices: An Analytical Approach

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Название: Self-Dual Gauge Field Vortices: An Analytical Approach

Автор: Tarantello G.

Аннотация:

Elliptic problems arise in the study of significant questions concerning vortices in various selfdual field theories, e.g., Chern — Simons and Electroweak theories. Despite progress in these directions, many open questions still remain and are examined in this work in connection with Liouville-type equations and systems.

Key topics unfold systematically beginning with the foundations of gauge theory and examples of selfdual vortices; chapters thereafter treat elliptic problems involving selfdual vortices, Ginzburg — Landau and Chern — Simons models, concentration-compactness principles, and Maxwell — Chern — Simons vortices.

To date there is no comprehensive examination of the subject. The primary orientation of the text is partial differential equations, but the reader should have knowledge of some basic tools in field theory. For graduate students and researchers in PDEs and mathematical physics.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2008

Количество страниц: 348

Добавлена в каталог: 13.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abelian–Higgs model      129
Abelian–Higgs string      288
Abrikosov      40 48
Adjont representation      14 15 19 26
Asymmetric vacuum      76
Bianchi identity      2 28
Blow-up point      181 182 194 243 270
Blow-up profile      227
Blow-up set      181 195
Bogomolnyi      1 5
Born–Infield theory      111
Bosonic sector      36
Brouwer degree      52
Cartan matrix      24 31 33 46 70 164
Cartan subalgebra      20 22—24
Cartan — Weyl basis      19 20
Cartan — Weyl generators      26 33
Cauchy — Riemann equations      12 43
Charge      3
Chern number      28
Chern — Pontryagin class      29
Chern — Simons energy      8
Chern — Simons field equations      127
Chern — Simons limit      129 164
Chern — Simons model      12 33 49 129
Chern — Simons parameter      6 8 9
Chern — Simons theory      1 6 283
Chern — Simons vortices      7 29 77 111 127 131 162 171 303
Chern — Simons — Higgs 6th-order model      1 8 75 169
Concentration-compactness principle      184 241 248
Concentration-compactness principle, condensed matter physics      6
Conformal factor      40 48
Conformal factor, conformal field theory      6
Conjugate representation      15 33
Connection      17
Cooper pairs      4 75
Cosmic strings      111 283
Coulumb gauge      43
Covariant derivative      17 60
CP(1)-model      164
Critical point      56 136
Critical value      56
Current      3 10 31 32 34
Curvature      2 17 28 283 284
de Rahm cohomology      29
Dirac measures      44 53 248
Dirichlet boundary conditions      247 303
Einstein’s equations      40 282 283
Electric charge      9 49 50 81 127 171
electric field      3
Electromagnetic interactions      2 3 19 37
Electromagnetism      19
Electroweak strings      40 41 48 51 282 284
Electroweak theory      1 19 35
Electroweak vortices      40 47 50 111 174
Elliptic regularity      76 114 177
Energy      4 32
Euler characteristic      68
Euler — Lagrange equations      3 8 10 30 31
Exponential      16 35 52
Flat torus      64
Fourier decomposition      114
Fredholm map      66 67 278
Gauge, field      2 13 17 18 36
Gauge, group      13
Gauge, invariance      34 43
Gauge, map      18
Gauge, potential      2 17
Gauge, theory      1 17
Gauge, transformations      3 12 38 43
Gauss, curvature      41 51 243 263 283
Gauss, law      4 7 11 32
Genus      253 256
Ginzburg — Landau model      1 13 52
Ginzburg — Landau theory      4
Ginzburg — Landau vortices      6 13
Gravitational constant      283
Gravity      40
Green’s function      68 247 263 272
Green’s representation formula      86 160 196 228 239
Harnack inequality      107 177 178 200 213
Heat flow      145
Hermitian conjugate      16
Higgs field      2 12 17 18 27 81 129
Hodge operator      28
Holomorphic      43 52 53 220
Homotopy      29
Implicit function theorem      113 254 285 299
inf+sup estimates      206 237
instantons      5 28
Internal symmetry      13 18
Jacobi identity      19
Jensen’s Inequality      67 132 140 158 160 193 256 264
Killing form      15 21 27
Lagrangean      3 6 10 18 30
Laplace — Beltrami operator      64 242 249
Laplacian operator      52
Leray — Schauder degree      67 252
Lie, algebra      13 14 18 21
Lie, bracket      14 27
Lie, group      1 13 14 17 18
Lioville, equation      52 60 112 212 285
Lioville, formula      65 112 158 212 220
Lioville, problem      111
Magnetic field      3 171
Magnetic flux      5 49 50 81 127
Mass scale parameter      10 31
Massive field      284 300
Maximal solution      92 96 137 144
Maximum principle      76 132 251
Maxwell — Chern — Simons — Higgs (MCSH) model      49 129 130
Maxwell — Chern — Simons — Higgs (MCSH) theory      9 10
Maxwell — Chern — Simons — Higgs (MCSH) vortices      11 12 129
Maxwell — Higgs equations      79
Maxwell — Higgs limit      163
Maxwell — Higgs model      1 7 12 29 49 76 129 303
Maxwell — Higgs theory      19 283
Maxwell — Higgs vortices      76
Maxwell, electrodynamics      6
Maxwell, equations      4 28
Mean field equation      64 249 253
Metric tensor      2
min-max      67 256
Minimal solution      137 138 144
Minkowski metric      7
Minkowski space      2 17 35
Momentum      7
Monopoles      30
Moser — Trudinger inequality      64 140 152 155 158 171 177 256 261
Neumann boundary conditions      247
Neutral scalar field      9 10 12
Nielsen — Olesen vortex      5 29
Non-abelian      1 5 19 31 33 130 164
Non-relativistic      1 12 34
Non-topological      65 76 111 126 129 130 145 165 168 248
Order parameter      4
Palais — Smale      56 57
Pauli matrices      25 35
periodicity      48
Pohozaev type identity      100 179 196 234
Potential field      2 36
Principal bundle      17
Principal embedding vacuum      130 164
Pseudo-gradient      57 145
Quantum Hall effect      6
Radially symmetric      100 127
Rank      20 129
Riemann metric      60
Riemann surface      41 61 249 283
Root      19 20
Scalar potential      3
Seiberg — Witten model      303
Self-gravitating      40 48 283 284
Selfdual equations      5 8 11 33 39
Selfdual regime      8 13
Selfdual structure      1 31
Semisimple group      15 16 21
Simple root vectors      21
Skew-symmetric      3 5 6
Sobolev inequality      58 104
Solitons      4 9
Space of moduli      29
Special orthogonal group      16
Special unitary group      16
static      4 5
Stereographic projection      62
Strong interactions      19
SU(n + 1)-vortices      72 165
Subharmonic function      85
Subsolution      92 136—138
Superconductivity      1 4 75
Superharmonic function      94
Supersolution      134 137
Symmetric vacuum      76
Symmetry breaking      10 31 54 288
Temporal gauge      4 7 28 29
Theta function      69
Time-dependent      9
Toda-functional      172
Toda-system      72 248 278
Topological degree      49
Topological solutions      126
Topological vortices      76 81 128
Total energy      49 81 127 283
Trace      15 23
Triple well potential      9
Unbroken vacuum      130 164
Unified theory      19
Unitary gauge      37 39
Vortex, number      51 76 77 300
Vortex, points      51 75 77 137 173
W-condensates      39
Weak interactions      19 37
Weierstrass function      65 158
Weinberg mixing angle      37 281
Yang — Mills equations      6 27
Yang — Mills fields      28 29 303
Yang — Mills model      5
Yang — Mills — Higgs equations      27
Yang — Mills — Higgs theory      26 29
’t Hooft      39 48 51 300
“Double-well” potential      3
“Mountain-pass”      56 103 139 141 145
“Moving planes”      55 212
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