Gomez C., Ruiz-Altaba M., Sierra G. — Quantum Groups in Two-Dimensional Physics :: Электронная библиотека попечительского совета мехмата МГУ

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Gomez C., Ruiz-Altaba M., Sierra G. — Quantum Groups in Two-Dimensional Physics

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Название: Quantum Groups in Two-Dimensional Physics

Авторы: Gomez C., Ruiz-Altaba M., Sierra G.

Аннотация:

This book is an introduction to integrability and conformal field theory in two dimensions using quantum groups. The book begins with a brief introduction to S-matrices, spin chains and vertex models as a prelude to the study of Yang-Baxter algebras and the Bethe ansatz. The basic ideas of integrable systems are then introduced, with particular emphasis on vertex and face models. Special attention is given to explaining the underlying mathematical tools, including braid groups, knot invariants and towers of algebras. The book then goes on to give a detailed introduction to quantum groups as a prelude to chapters on integrable models, two-dimensional conformal field theories and super-conformal field theories. The book contains many diagrams and exercises to illustrate key points in the text. This book will be of interest to graduate students and researchers in theoretical physics and applied mathematics interested in integrable systems, string theory and conformal field theory.

Язык:

Рубрика: Математика/Алгебра/Квантовые группы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1995

Количество страниц: 475

Добавлена в каталог: 26.03.2005

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Предметный указатель

$U_q(A_1^{(1)})$       56
      271
      52 55 57 97 107 190 196
$U_q(\mathscr{G})$       207
$U_q^{'}(sl(2))$       57
$\beta-\gamma$ system      305
$\mathscr{R}TT$ equation      38 39 52
$\sl(2,\mathbb{C})$ vacuum      285
$\theta$ functions      125
$\theta$ parameter      119 121 122
$\zeta$ function      106
3j symbol      see “Clebsch — Gordan coefficient”
6j symbol      200—201 319—323 381
ADE partition functions      338
Affinization parameter      56
Alexander—Conway polynomial      167 171 176 252 271
Anisotropy      14 21 25 45 66 74 75 77 102 110 121 129
Anomalous dimension      279
Antiferromagnetic state      72 75 78 82
Antipode      185 229 396
Auxiliary space      34 53 62 90
b-c system      305
Background charge      342
Baxter lattice      15
Baxterization      269
Bethe ansatz for descendants      61—64
Bethe ansatz for eight-vertex model      111—120 122
Bethe ansatz for higher spin      84 85
Bethe ansatz for nilpotcnt hamiltonians      245—249
Bethe ansatz for open chains      92—96
Bethe ansatz for XXX model      80—83
Bethe ansatz for XXZ chain      74—78
Bethe ansatz, algebraic      41—47 245
Bethe ansatz, coordinate      12 13 20 21 107
Bethe equations      44 64 96 120
Bethe reference state      10 12 20 42 63 93 118 120
Bethe root      75—83 85 104
Bethe string      79—83 103
Bi-algebra      40 57 185
Bi-colored graph      137 160
Bi-unitary matrix      178
Birman — Wenzl algebra      173
Block spin renormalization      275
Bogomolny soliton      435
Boltzmann weight      16 24
Boltzmann weight and $\mathscr{R}$ -matrix      35 109
Boltzmann weight and quasi-momenta      43
Boltzmann weight for boundaries      88
Boltzmann weight for descendants      65
Boltzmann weight for eight-vertex model      110 124 130
Boltzmann weight for face model      134 146
Boltzmann weight for fused face model      156
Boltzmann weight for Ising model      148
Boltzmann weightas vector fields      68
Boltzmann weightfor six-vertex model      17 23 67
Boost      2 160
Bootstrap      29—32
Borel subalgebra      189 394
Boundary operator      88 92 107
Braid group      48 139 165—196 250 323
Braid limit      49—53
Braiding matrix      203 319—323 349—353
Bratelli diagram      137—140 142 144 204
Brauer representation      161
BRS charge      429
Burau representation      171
c theorem      121 306
Cartan matrix      207
Casimir      194 229
Central charge      285 297 300
Central extension      104 106 121 122 215
centralizer      201 379
Charge conjugation      31 299 321
Checkerboard model      264
Chevalley basis      56 207
Chiral algebra      289 308
Chiral Potts model      252—268 271
Chiral primary field      427
Chiral ring      429 437
Chiral vertex operator      312 336 401 418
Clebsch-Gordan coefficient      197—200 417
Clock model      252
Co-adjoint action      232
Co-algebra      185
Co-associativity      184 219
Co-cycle      215
Co-multiplication      see “co-product”
Co-product      40 53 55 57 97 184 191 313 392
Co-unit      185 229 396
Commuting square      178 181
Conditional expectation      142 164 168 323
Conformal block      87 197 312
Conformal invariance      72 272
Conformal transformation      68
Conformal weight      287 297
Contour deformation      313 393 398—400
Corner transfer matrix      158—160 162—164 226 365 371
correlation length      272 276
Coulomb gas      340 345 379
Coupling constant      9 102
Coxeter graph      135 143 146—148 339
Coxeter number      147 162 381
CPT invariance      7
critical exponent      272 276 287
Crossing unitarity      91
Crystal base      227 379
Curie point      273
Current conservation      17
Decoupling of null vectors      291—299 320 332 343 358 378
Dedekind's $\eta$ function      331
Deformation parameter      53
Derivation      215 232
Descendant field      287
Descendant model      58
Difference property      3 38 39 50 76 109 258—260
Dilogarithm      301
Dirac sea      76 79 83 85 98 104
dispersion relation      71 72 83 300
Drinfeld's double      see “Quantum double”
Dual algebra      190
Dual Coxeter number      356
Dual lattice      151
Duality      308 319
Dynkin diagram      135 212—214 339
Eight-vertex model      108—124 136 155
Elementary excitations      72
Elliptic curve      109 110
Elliptic exponential      123 124 128
Elliptic functions      125—129
Elliptic nome      110 150 153 328
Energy-momentum tensor      281 288
entropy      103
Euler's pentagonal identity      337 369
Extended Yang-Baxter system      173 206
Face model and eight-vertex model      115
Face model as hidden symmetry in higher-spin chains      87—88
Face model, Boltzmann weights      134
Face model, chiral Potts      255
Face model, corner transfer matrix      365
Face model, fusion      155 164
Face model, restricted      145 154
Face model, Yang — Baxter equation      136
Factor      177—182
Factorization equations      5 8 13
Fan — Wu condition      122
Feigin — Fuks      see “Coulomb gas”
Fermat curve      258
Fermi surface      72
Fermion number      16 435
Ferromagnetic state      12 29 72

Fibonacci number      338
Finite-size scaling      286 300—302
Form factor      28—33
Four-Fermi interaction      102
Free energy in critical phenomena      273
Free energy, finite size behavior      300
Free energy,Kramers-Wannier duality      153
Free energy,minimal model      122
Free energy,one-dimensional Ising model      277
Free energy,six-vertex model      121
Free energy,spin— $\S$ chain      103 104
Free fermion, character      337
Free fermion, eight-vertex model      123 124
Free fermion, Ising model      31
Free fermion, nilpotent irreps      241
Free fermion, sine-Gordon      10
Free fermion, XX model      36
Free fermion,supersymmetry      418
Free field      340—341 see
Freudenthal — de Vries strange formula      368
Friedan — Shenker bundle      401
Fundamental construction      141 181 327
Fusion algebra      296—299
Fusion and quantum groups      378 81
Fusion and towers of algebras      324—327
Fusion matrix      319—321 352
Fusion rules      296 338 346
Galilean group      221
Gauss binomial formula      237 408
Gauss decomposition      233 359
Gaussian model      278 302
Goddard — Kent — Olive construction      364 425
Haldanc's conjecture      98 101
harmonic oscillator      220 250 271
Harmonic ratio      68 311
Hecke algebra      69 139 170 202 378
Hexagonal equation      115 321 336
High temperature expansion      153
Higher-spin chain      83 104
Higher-spin descendant      155 264
hole      79 81
Homfly polynomial      167 171
Homotopy group      165
Hopf algebra      184 220 392
Hopping parameter      26
Hubbard model      244 270
Hypergeometric function      311 370
Incidence matrix      134—137 141 146
Inclusion matrix      see “incidence matrix”
Inner derivation      232
Integrability      1 2 14 21 23 37 47 72 91 109 160
Integrable deformation      434
Integrable representation      413
Interaction round a face model      see “face model”
Intertwiner      58 89 234 265 313 355 413
IRF model      see “face model”
Irreducible representations,       194
Irreducible representations, affine $A_1^{(1)}$       56
Irreducible representations, cyclic      230 265—267
Irreducible representations, nilpotent      231 238
Irrelevant operator      270 287
Ising model, chiral Potts      252
Ising model, Boltzmann weights      148
Ising model, conformal blocks      348—350
Ising model, conformal weights      299
Ising model, eight-vertex model      121
Ising model, form factors      31—32
Ising model, one-dimensional      275
Ising model, Onsager algebra      261
Ising model, partition function      331 337
Jacobi elliptic function      78 109 127
Jacobi theta function      126
Jacobi's triple product identity      337 369
Jones polynomial      167 170 171 206
Jordan — Wigner transformation      26 102 123 241
Kac determinant      292
Kac formula      292 295 346 391
Kac — Moody algebra      213 216 290 363 376
Kac — Moody character      364
Killing vector      38 68 258 288
Kink operator      26
Knizhnik — Zamolodchikov equation      148 356 367 376 382 419
Knot      165
Kramers — Wannier duality      31 150—153 260
Kronecker's theorem      146
Landau Ginsburg lagrangian      304
Landau — Ginsburg super-potential      432
Lattice hamiltonian      22 23 46 65 69 84 92
Lattice momentum      10 22 23 46
Lee — Yang edge singularity      298
Leibnitz's chain rule      231
Leningrad formula      86—87
Level      216 291
Levi — Civita tensor      106
Lie bracket      215
Link      165
Link invariant      197
Local state probabilities      366
Loop algebra      212
Lorentz group      221
Lorentz spin      2 287
Low lying excitation      71 72 78 82 98 105
Low temperature expansion      151
magnetization      273
Majorana fermion      31
Majumdar — Ghosh hamiltonian      106
Mandelstam variables      318
Marginal operator      270 287
Markov move      168
Markov trace      122 139 142 144 164 168 205 327 385
Mass gap      71 72 98 102 106 261
Maximal root      223
Minimal model and quantum group      413
Minimal model and XXZ chain      106 302
Minimal model, and Landau — Ginsbura      304
Minimal model, central extension from finite size      121
Minimal model, fusion rules      299
Minimal model, Kac formula      297
Minimal model, N=0, 1, 2 models      428
Minimal model, Rocha — Caridi formula      330
Mobius transformation      285
Modular invariance      330 339
Modular matrix      329 338 383
Modular parameter      328
Modular transformation      329
Moduli space      315
Momentum operator      21
Monodromy invariance      310
Monodromy matrix      38 51 61 65 89 116 245
Monodromy transformation      310
Morse function      433
Mutual locality index      28
Neel state      27 102
Neveu — Schwarz super-algebra      423
Normal order      188 340
Null descendant      292
Null vector      291 295 343 358 387
Number operator      18
Ocneanu's string operator      144
Onsager algebra      261
Operator formalism      308
Operator product expansion      285 293 340 350 423
Order and disorder operators      32
Order parameter      273
Parity symmetry      53
Partition function      17 151 152 159 278
Path representation      225
Pauli exclusion principle      11 80 270
Pentagonal equation      200
Permutation map      47 49 68 195

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