Di Francesco P., Mathieu P., Senechal D. — Conformal field theory :: Электронная библиотека попечительского совета мехмата МГУ

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Di Francesco P., Mathieu P., Senechal D. — Conformal field theory

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Название: Conformal field theory

Авторы: Di Francesco P., Mathieu P., Senechal D.

Аннотация:

Filling an important gap in the literature, this comprehensive text develops conformal field theory from first principles. The treatment is self-contained, pedagogical, and exhaustive, and includes a great deal of background material on quantum field theory, statistical mechanics, Lie algebras and affine Lie algebras. The many exercises, with a wide spectrum of difficulty and subjects, complement and in many cases extend the text. The text is thus not only an excellent tool for classroom teaching but also for individual study. Intended primarily for graduate students and researchers in theoretical high-energy physics, mathematical physics, condensed matter theory, statistical physics, the book will also be of interest in other areas of theoretical physics and mathematics. It will prepare the reader for original research in this very active field of theoretical and mathematical physics.

Язык:

Рубрика: Физика/Квантовая теория поля/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 890

Добавлена в каталог: 16.08.2005

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Предметный указатель

$SL(2, \mathbb C)$       114 747
$SL(2, \mathbb Z)$ modular group      338
algebra      227
$\mathbb Z_2$ orbifold      354 370 777
$\mathbb Z_2$ orbifold, at rational square radius      406
$\mathbb Z_2$ orbifold, operator content      783
$\varphi^4$ theory      65
$\varphi^4$ theory renormalization of      86
$\zeta$ -function regularization      172 341
ADE classification      813
ADE classification $\widehat{su}(2)$ modular invariants      756
ADE classification of $\widehat{su}(2)$ modular invariants      741
ADE classification of $\widehat{su}(3)$ modular invariants      743
ADE classification of graphs      372
ADE classification of integer matrices      399
ADE classification of minimal models      265
ADE classification of modular invariants      372
Adjacency matrix      373 512 757
Adjoint representation      491
Admissible representations character of      828
Admissible representations conjugated      831
Admissible representations fusion rules of      832
Admissible representations of $\widehat{su}(2)$       827
Admissible representations of generic affine Lie algebra      840
Affi e roots      560
Affine branching rules      597
Affine Cartan-Weyl basis      558
Affine character      581
Affine character modular properties      591
Affine Chevalley basis      564
Affine coroots      561
Affine Dynkin diagram      562
Affine Dynkin label      566
Affine embedding      596 733
Affine embedding level of the embedded algebra      596
Affine fundamental weights      564
Affine Kostant multiplicity formula      613
Affine Lie algebra      559 623
Affine Lie algebra modular S matrix      591
Affine Lie algebra modular T matrix      591
Affine Lie algebra singular vectors in      634
Affine Serre relations      564
Affine simple roots      561
Affine singular vector      577
Affine weight      560
Affine weight multiplicities      578
Affine weight system      578
Affine Weyl chamber      567
Affine Weyl group      566
Affine Weyl vector      566
Anharmonic ratio      99 106 117
Anticommutator      21 131
Antiperiodic boundary conditions boson      164
Antiperiodic boundary conditions fermions      169
Associated Weyl group      844
Asymptotic field      152
Basic fundamental weight      565
Basic representation      576
Belinfante tensor      46
Berenstein — Zelevinsky triangles      528 708
Bernoulli polynomials      173
Bessel function      34
beta function      83
Bezout’s lemma      396
Binomial distribution      90
Boltzmann distribution      61
Bond percolation      427
Bootstrap      185
Boson      15—21 128—129 159—168
Boson at self-dual radius      388
Boson charged Fock space of      321
Boson charged Fock space of at rational square radius      405 587
Boson charged Fock space of character      587
Boson charged Fock space of on a cylinder      434
Boson multicomponent      352
Boson on the cylinder      159
Boson on the cylinder, with fixed boundary conditions      437
Boson parity transformation of      436
Boson partition function of      340
Boson propagator      33
Boson Verma module of      203
Boson vertex operators      see “Vertex operators”
Bosonization non-Abelian      646
Bosonization on the plane      447
Bosonization on the torus      464
Boundary conditions fixed      421 437
Boundary conditions homogeneous      413
Boundary conditions Neveu-Schwarz      169; see “Neveu — Schwarz”
Boundary conditions Ramond      169; see “Ramond”
Boundary operators      421—427
Boundary operators percolation and      430
Branching functions      801
Branching functions, modular transformations      804
Branching of group centers      599
Branching of outer automorphism groups      599
Branching rules      534
Branching rules affine      597
Branching rules generating function      536
Branching rules regular embedding      538
BRST charge in minimal models      324
BRST cohomology      320
BRST symmetry      320
BRST symmetry in minimal models      325
c = 1 models      349—356
c = 1 models, classification      779
c = 1 models, correlators, on the torus      484
c = 1 models, operator content      782
C-algebra      761
canonical ensemble      62
Cartan matrix      495 540
Cartan matrix affine      561
Cartan subalgebra      491
Cartan subalgebra affine      559
Cartan — Weyl basis      491
Cartan — Weyl basis affine      558
Casimir energy      see “Free energy” “Finite-size
Casimir operator      511
Cauchy determinant formula on the plane      483
Cauchy determinant formula on the torus      485
Center of a Lie group      574
Center of a Lie group relation with the group of outer automorphisms      574 596
Center of RCFT      679
Central charge      135
Central charge of minimal models      216
Central charge, coset models      797
Central charge, in Virasoro algebra      156
Central charge, physical meaning of      138’
Central charge, trace anomaly and      140
Central charge, transformation of the EM tensor and      136
Central charge, WZW models      626
Central element      557
Chamber      501
CHARACTER      517
Character block-      365
Character boson compactified on a circle      587
Character coset      801
Character decomposition      801
Character decomposition for nonunitary $\widehat{su}(2)$ diagonal cosets      837
Character extended      365 385
Character in WZW model      637
Character method      523
Character method affine extension      679
Character of admissible representations $\widehat{su}(2)$       828
Character of admissible representations modular transformations      830
Character of integrable highest-weight representations      581
Character of irreducible Verma module      242
Character Virasoro      203
Character, $\widehat{su}(2)_k$       585
Character, Demazure formula      549
Character, Heisenberg module      587

Character, highest-weight representation (Lie algebra)      517
Character, mimimal models      810
Character, modular transformation of      359
Character, normalized      584
Character, specialized      584
Character, Weyl formula      518
Character, Weyl — Kac formula      581
Charge conjugation for admissible representations      831 845
Charge conjugation matrix      593
Charge conjugation matrix of admissible representations      832
Charge conserved      41
Charge, generator of symmetries      44
Charged bosonic Fock space      321 332
Chebyshev polynomials      260 531 699
Chebyshev polynomials, generalized      533 553
Chebyshev polynomials, generating function      532
Chevalley basis      497
Chevalley basis affine      564
Chiral bosonization on the plane      447
Chiral bosonization on the torus      471
Chiral vertex operators      295
Classical algebra      498
Classical limit      27
Classical limit of the quantum KdV equation      195
Classical limit of the Virasoro algebra      197 243
Classification of conformal field theories      9
Classification of embeddings      537
Classification of minimal models      372
Classification of modular-invariant partition functions      12
Classification of modular-invariant WZW partition functions      720
Classification of RCFTs      390 797
Classification of simple Lie algebras      498
Classification of universality classes      6
Clock model      225
Cluster property      147
Cocycle      672
Coherent states of fermions      28
Coherent states of harmonic oscillator      187
Comark      496 540
Comark affine      562
Commutator, contour integrals and      154
Compact real form      498
Compactification (string theory)      354
Complex coordinates      112
Conformal algebra, in $d\geq 3$       98
Conformal anomaly      see “Central charge”
Conformal blocks      185 376 405
Conformal blocks in Coulomb-gas representation      327
Conformal blocks in WZW models      644
Conformal blocks monodromy properties on the torus      379
Conformal blocks of bosonic electromagnetic operator two-point function on a torus      484
Conformal blocks of four-point functions      314
Conformal blocks of four-point functions involving $\phi_{(1,3)}$       330
Conformal blocks of four-point functions involving $\phi_{(2,1)}$       308
Conformal blocks of Ising energy one-point function on the torus      455
Conformal blocks of Ising energy two-point function on a torus      458
Conformal blocks of Ising spin two-point function on a torus      461
Conformal blocks of n-point functions      315
Conformal blocks on higher genus      318
Conformal bootstrap      9 185
Conformal branching rules      735
Conformal charge      155
Conformal dimension      116
Conformal dimension in minimal models      216
Conformal dimension of WZW primary fields      630
Conformal embedding      733 734
Conformal embedding in $d\geq 3$       98
Conformal embedding, branching rules      735 770
Conformal embedding, modular invariants      739
Conformal families      178
Conformal gauge      144
Conformal generators in d = 2      114 155
Conformal group      95—99
Conformal group in d = 2      112
Conformal group representations in $d\geq 3$       99
Conformal invariance on the cylinder      410
Conformal invariance on the unit disk      434
Conformal invariance on the upper half-plane      413
Conformal invariants      see “Anharmonic ratio”
Conformal transformation      95
Conformal transformation in $d\geq 3$       97
Conformal transformation in d = 2      113
Conformal transformation local      113
Conformal transformation of energy-momentum tensor      136
Conformal transformation special      97
Conformal transformation, global      113
Conformal Ward identity      see “Ward identity”
Congruence classes      503
Congruence vector      503 540
Conjugacy classes      503
Conjugate representation      510
Conjugation invariant      744
Connected functional      51 141
continuum limit      19 23 65 82
Coroot lattice      502
Coroots      496
Coroots affine      561
Correlation functions      30
Correlation functions connected      64
Correlation functions equations of motion for      58
Correlation functions four-point      see “Four-point function”
Correlation functions in WZW model      638
Correlation functions of vertex operators      328
Correlation functions three-point      see “Three-point function”
Correlation functions transformation of      42
Correlation functions two-point      see “Two-point function”
correlation length      68
Correlation length divergence of      5 69
Correlation length of massive boson      35
Correlation length relation with mass      90
Coset construction      799
Coset description of nonunitary minimal models      833
Coset description of unitary minimal models character decomposition      808
Coset description of unitary minimal models, fusion rules      812
Coset description of unitary minimal models, modular invariant partition functions      813
Coset description of unitary minimal models, modular S matrix      811
Coset partition function      807
Coset rational conformal field theory      806
Coset S matrix      805
Coset T matrix      805
Coset unitary minimal models      807
Coulomb-gas representation      294—328
Coulomb-gas representation conformal blocks in      327
Coulomb-gas representation minimal models on a torus      406
Coxeter group      500
Critical exponents      69
Critical exponents $\eta$       105
Critical exponents surface      419
Critical phenomena      4 67—74
Critical phenomena quantum      6
Critical surface      76
Cross-ratios      see “Anharmonic ratios”
Crossing probabilities (percolation)      430
Crossing symmetry      186 644
Cumulant expansion      79
Current algebra      623
Current dilation, or scale-invariance      102
Current for massless boson      297
Current Noether      41
Curvature      57 140
Cyclic group      778
Cylinder theory defined on a      139 410
Dedekind $\eta$ function      204 394
Deep inelastic scattering      7
Defect line (magnetic)      351
Dehn twists      339
Demazure character formula      549
Denominator identity (Macdonald — Weyl)      582
Density operator      66
Depth      690

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