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

Perron — Frobenius theorem      73 78 145
Perturbed chiral ring      435
Perturbed tagrangian      307
Phase shift      12
Phase space      1
Phase transition, first and second order      273 281
Pochhammer contour      370 410
Poincare algebra      224
Poisson bracket      1 132
Polynomial equations      321 328
Potts model      162 253 261 298
Primary field      289 291 301 341
Projective representation      285
Propagator      318 328 340
Puncture      314
q-intertwiner      371
q-Knizhnik — Zamolodchikov equation      371
q-number      193
Quantum determinant      67 123 132
Quantum dimension      326 337 384
Quantum double      188 221 400
Quantum group and spin chain hamiltonian      97 107
Quantum group as Yang — Baxter algebra      51
Quantum group,       52 55 189
Quantum group, affine      56 90 162 214
Quantum group, contour representation      392—396
Quantum group, Hopf algebra      184—186
Quantum group, knots      171
Quantum group, quasi-triangular Hopf algebra      186
Quantum space      34 53 62 90
Quasi-Hopf algebra      218 227 382 420
Quasi-momentum      12
R-matrix for descendants      59
R-matrix in Coulomb gas      396—400
R-matrix in vertex models      35
R-matrix, affine      217—218
R-matrix, an incomplete catalog      208
R-matrix, as intertwiner      54—55 60 234
R-matrix, classical      376
R-matrix, eight-vertex      112 129
R-matrix, infinite-dimensional      251
R-matrix, Jimbo's      50
R-matrix, nilpotent      235 40
R-matrix, permuted      66
R-matrix, six-vertex      37 45 58 91 366
R-matrix, symmetry properties      90
R-matrix, universal      55 66 186 193
Radial quantization      283
Ramond ground state      429
Ramond super-algebra      425
Rapidity      2 9 27 33 45 66 75 118 255 257
Rational conformal field theory      261 297
Reflection coefficient      95
Reidemeister move      166 168 198
Relevant operator      280 287
Renormalization group      272 275 279
Representation of $U_q(A_1^{(1)}$       56
Representation of $U_q(st{2))$       55
Representation of braid group      50 138
Representation of Sklyanin algebra      131
Representation of Temperley — Lieb — Jones algebra      140 145
Representation of Yang — Baxter algebra      40 41 53 58
Representation, higher-spin      84
Reshetikhin criterion      70 271
Restricted face model      120 155
Reversal symmetry      17
Ribbon Hopf algebra      197 251 384
Riemann surface      288 314
Riemann — Hilbert problem      320 377
Rocha — Caridi formula      330
Root of unity, Bethe ansatz      88 107 121
Root of unity, chiral Potts      263—268
Root of unity, conformal field theory      382
Root of unity, face models      147 154
Root of unity, quantum groups      228—231
RSOS model      see “face model”
S-matrix for solitons      136
S-matrix for spin wave      25
S-matrix,      4
S-matrix, analyticity      29
S-matrix, crossing symmetry      7 8 90
S-matrix, elliptic      121
S-matrix, factorizability      3 4
S-matrix, real analyticity      7
S-matrix, unitarity      7 8 69 90
Scale invariance      281
Scale transformation      272
Scaling function      50 273
Schur's lemma      230 232
Schwarzian derivative      285 304 423
Schwinger term      285
Screened vertex operator      386—392 397
Screening current      345 386 402
Self-dual chiral Potts model      261
Serre relations      207 394 418 420
Sewing construction      314
Sewing parameter      315
Shift operator      10 22 69 180
Sine-Gordon      9 10 27 102 366 420
Singularity theory      437
Six-vertex model      15—17 39 45 67 74 270
Skein relations      167 210
Sklyanin algebra      130 132
Sklyanin equations      91
SL(2) invariance      343
Smirnov's program      28—33
Solid on solid model      see “face model”
Soliton      9 29 137 434
SOS model      see “face model”
Spec $Z_\epsilon$       233
Specific heat      301
Spectral flow      426
Spectral parameter      50 112 266
Speed of sound      104

Spin chain      10 14
Spin chain, open      92
Spin model      180 252 255
Spin parity      250
Spin wave      11 12 19
Spin—1 hamiltonian      70 98 107 242
Star-triangle equation      24 183 257
String hypothesis      79 86
String operator      144
Structure constant      312 430
Structure function      289
Subfactors      140
Sugawara construction      355 363
Super-conformal algebra      426
Super-conformal field theory      422
Super-conformal transformation      423
Super-integrable chiral Potts model      261
Super-potential      429 432
Super-symmetry      420 422 425
Super-Virasoro algebra      423
T invariance      90
Termperley — Lieb-Jones algebra, Brauer representation      161
Termperley — Lieb-Jones algebra, conformal field theory      323—327 378
Termperley — Lieb-Jones algebra, definition      139
Termperley — Lieb-Jones algebra, face models      145
Termperley — Lieb-Jones algebra, fundamental construction      140—144
Termperley — Lieb-Jones algebra, Markov moves      168
Termperley — Lieb-Jones algebra, open XXZ chain      98
Termperley — Lieb-Jones algebra, relation to Hecke      139
Termperley — Lieb-Jones algebra, spin models      181
Thermal subalgebra      297 309 331
Thermodynamic limit      17 73 75 83 103 104 153 159
Time reversal      31
Topological field theory      430 432
Torus      328 332
Tower of algebras      141 323 327 337
Transfer matrix and $_mathscr{R}$ -matrix      34 35
Transfer matrix and monodromy matrix      38
Transfer matrix, corner      see “corner transfer matrix”
Transfer matrix, derivatives      69
Transfer matrix, descendant models      61 65
Transfer matrix, eigenvalues      20 44 64
Transfer matrix, eight-vertex model      117
Transfer matrix, face models      135 138
Transfer matrix, nilpotent models      240
Transfer matrix, open chain      90
Transfer matrix, six-vertex model      18 43
Transfer matrix, spin models      180
Transfer matrix, twisted boundary conditions      106
Tricritical Ising model      298
Truncation in Bethe ansatz      87 88
Truncation in Coulomb gas      413
Truncation in face models      155
Truncation in minimal models      297—299
Truncation in representation theory      415
Twist operator      219 414
Twisted energy-momentum tensor      429
Uniformization for S-matrix      9
Uniformization for six-vertex model      23 37 45
Uniformization, chiral Potts      258
Uniformization, rapidity of solitons      29
Universal enveloping algebra      53 189
Universality class      272 287
Unrestricted graph      154
Vacancy      81
Valence bond solid      99—101 106
Verlinde's theorem      339 384 415
Verma module      287 291 295
Vertex model      15 23
Vertex operator      341 375
Vertex-face map      115 132 136 147 156
Virasoro algebra      285 286
Virasoro character      328 333 337 365 370
Virasoro irreducible representation      289 291
Von Neumann — Jones index      177
W-algebra      419
Wakimoto construction      362 367
Ward identities      292 294 345
Wess — Zumino model      88 304 336 382 401 418
Wick theorem      340
Writhe number      170
XX model      25 29 241 244
XXX model      14 25 47 70 71 86 97 111
XXZ model      14 22 25 27 69 73 75 93 102 110 162 163
XY model      123 124 307
XYZ model      14 110
Yang — Baxter algebra      39 40 51 59 116
Yang — Baxter equation and knots      166
Yang — Baxter equation for Boltzmann weights      24
Yang — Baxter equation for conformal blocks      320
Yang — Baxter equation for descendants      60
Yang — Baxter equation for eight-vertex model      110 115
Yang — Baxter equation for face models      115 135
Yang — Baxter equation for free fermions      124
Yang — Baxter equation for fused face model      156—158
Yang — Baxter equation for lsing model      148
Yang — Baxter equation for nilpotent irreps      240
Yang — Baxter equation for permutations      69
Yang — Baxter equation for spin models      183
Yang — Baxter equation for spin waves      13
Yang — Baxter equation for vertex models      24 36
Yang — Baxter equation from commuting squares      179
Yang — Baxter equation in the contour representation      398
Yang — Baxter equation universal      187 195
Yang — Baxter equation with afiine parameter      217
Yang — Baxter equation, classical      210 356 367
Yang — Baxter equation, operator      36 37
Yang — Baxter equation, permuted      48 49
Yang — Baxter equation, S-matrix      5
Yang — Baxter operator      138 140 159 323
Yangian      223
Young diagram      170
Young tableau      204
Z symmetry      5 91
Zamolodchikov algebra and operators      6 8 28 68

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