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

Depth rule      690
Descendant states      158
Diagonal coset      800 802
Diagonal invariant      722
Diagram of dimensions      215
Differential equations for correlation functions      247
Differential equations for correlation functions on a torus      456
Diffusion equation      145
Dihedral group      778 779
Dilation      38
Dilation conserved current for      102 109
Dimension of a Lie algebra      490 540
Dimension of a representation      519 522 551
Dimensional analysis      84
Dirac fermion      447
Disorder operator      441 451
Disorder operator, two-point function on a torus      463
dispersion relation      19 23
Divergences in quantum field theory      20
Dominant affine weight      566 576
Dominant weight      502
Doubling identities      479
Dual Coxeter number      496 540 625
Dual lattice      503 603
Duality      237 332 673
Duality boson      352
Duality in Ising model      441
Duality level-rank      702
Dynkin diagram      497 540
Dynkin diagram affine      562
Dynkin index of a representation      512
Dynkin label      498
Dynkin label affine      566
Electric charges (boson)      351
Electromagnetic operator      467
Elementary couplings Berenstein — Zelevinsky triangles      708
Elementary couplings for fusion rules      707
Elementary couplings for tensor products      707
Elementary excitations      19
Elliptic functions      477—479
Elliptic integrals      432
Embedding branching rules      534
Embedding conformal      733 770
Embedding index      535 597 799
Embedding Lie algebra      534
Embedding maximal      537
Embedding projection matrix      535
Embedding regular subalgebra      538
Embedding semisimple      770
Embedding special subalgebra      539
Embedding Verma modules coset      839
Energy average      62
Energy gap, and finite sizes      412
Energy-momentum tensor      45
Energy-momentum tensor Belinfante      46 109
Energy-momentum tensor of complex fermion      147
Energy-momentum tensor of free boson      128
Energy-momentum tensor of real fermion      131
Energy-momentum tensor of reparametrization ghosts      134
Energy-momentum tensor of simple ghosts      135
Energy-momentum tensor on the cylinder      139
Energy-momentum tensor OPE of      129 132
Energy-momentum tensor Sugawara construction      626
Energy-momentum tensor T and $\bar T$       120
Energy-momentum tensor technique, for torus correlators      459
Energy-momentum tensor traceless      101 107 110
Energy-momentum tensor, as variation of the action      49
Energy-momentum tensor, conformal transformation of      136
Energy-momentum tensor, mode expansion of      155
Energy-momentum tensor, quantum definition of      51
Equations of motion      58
Ergodic hypothesis      61
Euclidian formalism      31
Euclidian lattice      602
Euler function      158 204
Euler — Jacobi identities      612
Even lattice      352
Evolution operator      26
Exceptional algebra      498
Exceptional groups      779
EXPONENT      512
Exponent Lie algebra      540
Extended algebra      589
Extended Cartan matrix      561
Extended characters      365 385
Extended chiral algebra      745
Extended Dynkin diagram      538
Extended fusion rules      783
Extended fusion rules in $(E_6, A_{p-1})$ model      401
Extended fusion rules in $(E_8, A_{p-1})$ model      401
Extended fusion rules in Potts model      387
Extended fusion rules in tricritical Potts model      400
Extended S matrix of three-state Potts model      386
Extended symmetries fusion rules and      384
Fermion      21—25 109 129—132 168—173
Fermion coherent states of      28
Fermion complex      147 447
Fermion Dirac      447
Fermion doubling      24
Fermion Ising model and      221
Fermion modular-invariant partition function      349
Fermion on a cylinder      168
Fermion on the torus      344
Fermion propagator on a torus      457
Feynman diagrams      20
Field decoupling of      212
Field identification      801
Field identification canonical chain of      836
Field identification nonunitary $\widehat{su}(2)$ diagonal cosets      835
Field meaning of      104
Field primary      115
Field quasi-primary      116
Field secondary      116 179
Finite Lie algebra      559
Finite reducibility      599
Finite reducibility, theorem      739
Finite size correction      413 421
Finite subgroups SU(2)      778 780
Finite-size correction      139
Finite-size scaling      412
Finite-temperature corrections      412
First intersections      211
Fisher’s law      73
Fixed point      76 99 803
Fixed point hyperbolic      76
Fock modules $\widehat{su}(2)_l$       655
Fock space      20 163
Four-point function general form in d = 2      117
Four-point function in $d\geq 2$       106
Four-point function involving $\phi_{1,3}$       330
Four-point function involving $\phi_{1,3}$ of Ising energy and spin fields      287 331 481
Four-point function involving $\phi_{1,3}$ of WZW current      670
Four-point function involving $\phi_{1,3}$ of Yang-Lee model      287
Four-point function involving $\phi_{2,1}$       311
Four-point function of free boson      147
Free energy      62
Free-fermion representation $\widehat{so}(N)_l$       647
Free-fermion representation $\widehat{so}(N)_l$ characters      650
Free-fermion representation $\widehat{so}(N)_l$ primary fields      649
Free-fermion representation $\widehat{su}(N)_l$       652
Free-fermion representation of WZW models      647
Free-fermion representation WZW models      652
Free-field representation of WZW models      646
Freudenthal multiplicity formula      509
Freudenthal — de Vries strange formula      520
Functional integrals      see “Path integrals”
Fundamental affine Weyl chamber      567
Fundamental chamber      501
Fundamental domain      339
Fundamental weight      498

Fundamental weights affine      564
Fusion algebra      258
Fusion algebra associativity of      258
Fusion algebra attached to a graph      290
Fusion algebra matrix form of      258
Fusion coefficients      676
Fusion coefficients $\widehat{su}(2)_k$       684
Fusion coefficients $\widehat{su}(3)_k$       693
Fusion coefficients action of outer automorphism      677
Fusion coefficients relation to tensor-product coefficients      679
Fusion coefficients symmetries      677
Fusion coefficients threshold level      691
Fusion numbers      257
Fusion potential      699
Fusion rules      214 676
Fusion rules algorithm      681
Fusion rules character method      679
Fusion rules compactified boson      783
Fusion rules depth rule      690
Fusion rules elementary couplings      707
Fusion rules extended symmetries and      384
Fusion rules for admissible representations      832
Fusion rules in Ising model      235
Fusion rules in minimal models      217 255 400
Fusion rules Kac — Walton formula      681
Fusion rules modular invariance and      374
Fusion rules Weyl determinant method      697
Galois block-diagonal invariant      754
Galois permutation invariant      755
Galois symmetry      749
Galois transformation      749.
Gaussian Integrals      51
Gaussian model      65 84
Gelfand — Tsetlin pattern      516
Generalized ADE diagrams      764 767
Generalized Chebyshev polynomials      533 553
Generalized theta functions      582
Generalized theta functions modular transformation properties      604
Generating function for branching rules      536
Generating function for Chebyshev polynomials      532
Generating function fusion coefficients      776
Generating function tensor-product coefficients      716
Generating functional      33
Generator conformal      see “Conformal generators”
Generator of modular group      339
Generator of rotations      40
Generator of symmetry transformation      39
Generator of translations      39
Ghosts      132—135 661
Ghosts generalized      148
Ghosts reparametrization      132
Ghosts simple      135
Giambelli formula      696 697 715
Goddard — Kent — Olive (GKO) construction      800
Gordon identities      672
Grade      578
Grading operator      558
Gram matrix      206 235
Graph algebra      756
Graph subalgebra duality      761
Graph subalgebra duality equivalence relation      761
Graph subalgebra extended fusion rules and      759 767
Graph subalgebra modular invariants for $\widehat{su}(3)$ and      766
Graphs ADE classification of      372
Grassmann variables      52
Grassmann variables, complex      24
Grassmann variables, dynamics of      21
Group center branching rules      599
Group of outer automorphisms      571
Haffnian      449 483
heat capacity      62
Heat kernel      143 145 148
Height of a representation      539
Height vector      539 540
Heisenberg algebra      559
Heisenberg model      6 480
Heisenberg model classical      64
Hermitian conjugation      152
Hermitian product      152
Highest root      496 540
Highest-weight representation      201 508
Highest-weight representation affine      575
Highest-weight representation character (Lie algebra)      517
Highest-weight state      204 508
Hook      557
Hypergeometric equation      285 329
Hypergeometric function      308
Hypergeometric function properties      285
Icosahedral group      778 779
Ideal      289
Images, method of      416
Imaginary root      561
Index of a representation      512
Index of embedding      535
Integrable representation      577 634
Integral weight      498
Irreducible module      508
Irreducible representation      490
Irrelevant parameter      77
Ising model      62 439—476
Ising model on a triangular lattice      77
Ising model with a boundary      417
Ising model, diagonal coset description      814
Ising model, as minimal model      221
Ising model, boundary operators of      426
Ising model, characters in      242
Ising model, disorder operator      441 451
Ising model, energy correlator, upper half-plane      435
Ising model, one-dimensional      91
Ising model, orbifold formulation      785
Ising model, parafermionic description      821
Ising model, parity transformation of      435
Ising model, phase transition      68
Ising model, singular vectors of      236
Ising model, spin-energy correlator      436
Ising model, transfer matrix      92
Ising model, tricritical      222
Ising spin chain      479 608
Jacobi triple-product identity      390 672
Jordan — Wigner transformation      480
Josephson’s law      73
Kac determinant      207 240
Kac table      217
Kac — Moody algebra      559
Kac — Walton formula      681
Killing form      492
Knizhnik — Zamolodchikov equation      632 638
Kostant multiplicity formula      552
Ladder operator      491
Landau — Ginzburg theory for minimal models      231
Landau — Ginzburg theory for the Yang — Lee singularity      220
Laplacian      140
Lattice      352 502 602
Lattice coroot      502
Lattice dual      503 603
Lattice Euclidian      602
Lattice root      502
Lattice self-dual      503
Lattice weight      502
Length of state in a Verma module      210
Length of Weyl reflection      502
Level      158
Level (affine Lie algebras)      565
Level in Verma module      202
Level-rank duality      702
Lie algebra      490
Lie algebra embedding      534
Lie algebra, affine      559
Lie algebra, dimension of      490
Lie algebra, properties      540

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