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| Kohno T. — Conformal Field Theory and Topology |
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| Предметный указатель |
Action integral 1
Admissible labelling 51 85
Affine Lie algebra 18
Affine Lie algebra, of type  23
Algebraic constraint 46
Anti-symmetry 15 155
Arnold relations 77
Asymptotic, expansion 143
Asymptotic, region 83
Birkhoff theorem 40
Blackboard framing 91
Borel — Weil theory 6
Bosonic field 152
Braid group 76
Cabling 98
Cancellation of two critical points 94
Cartan — Killing form 24
Casimir element 24 77
Central charge 28
Central extension, of a loop algebra 18
Central extension, of a loop group 35
Central extension, of Laurent polynomial vector fields 20
Character of an affine Lie algebra 70
Chen's iterated integral 130
Chern — Simons, functional 11 121
Chern, class 4 20
Chern, form 4 20
Chiral vertex operator 62
Chord diagram 128
Chord diagram, on a surface 161
Classical field theory 7
Clebsch — Gordan quantum 49
Clebsch — Gordan rule 25
Cobordism 110
Cochain group 15
Cocycle, 2-cocycle condition 15
Cocycle, 2-cocycle for a loop algebra 17
Cocycle, 2-cocycle for Laurent polynomial vector fields 19
Cohomology, of Lie algebras 16
Coinvariant tensors 45
Complex line bundle 3 20
Complex line bundle, over the loop group 22 33
Configuration space 52 75
Conformal, block bundle 56
Conformal, invariance 59
Conformal, weight 29
Connection 3
Connection, matrix 83
Connection, on a complex line bundle 20
Contour integral 66
Conway polynomial 136 160
Covariant derivative 3 143
Curvature 79 121
Cut system 112
Dehn, surgery 104
Dehn, twist 113
Derivation 2
descendent 62
Diagonal action 43
Differential 16
Dilatation 60 68
Dilogarithm 137
Discriminant set 127
Drinfel'd associator 84 139
Dual line bundle 34
Dual representation 25 27
Elementary, connection matrix 86
Elementary, fusing operation 86
Elementary, tangle 91
Energy 29
Energy momentum tensor 64
Euler operator 60
Euler — Lagrange equation 1
External edge 51
Fermionic field 152
Feynman diagram 151
Feynman's path integral 8 42
Field 7
First Chern class 4 20
First Chern form 4 20
Flat connection 55
Four term relation 130
Framing 91 95
Framing, blackboard 91
Framing, independence 130
Fuchsian differential equation 84
Fundamental line bundle 23 33
Fusion, algebra 71 98
Fusion, rule 49
Gauge, fixing 152
Gauge, group 10 36 121
Gauge, invariance 62
Gauss formula for linking numbers 149
Gauss integral 143
Gluing axiom 9
Grassmann variables 152
Gravitational Chern — Simons invariant 153
Green form 149 153
Group of diffeomorphisms 18
Group of diffeomorphisms, of the unit circle 18
Hamiltonian 2 3
Hamiltonian, vector field 2
Handlebouy 116
Harmonic map 7
Heegaard splitting 117
Heisenberg equation 4
Highest weight, representation 24
Highest weight, representation with level fc 26
Highest weight, vector 24 26
Holonomy, of a complex line bundle 21
Holonomy, of the KZ connection 80
Hopf link 106
Horizontal section, of a complex line bundle 21
Horizontal section, of a conformal block bundle 57 58
Integrable, highest weight module 27
Integrable, subbundle 6
Isolated chord 129
Iwahori — Hecke algebra 88
Iwahori — Hecke algebra, representation 89
Jacobi identity 2 15 155
| Jones polynomial 97
Jones polynomial, two variable 136
Kahler polarization 6 125
Kirby moves 105
Knizhnik — Zamolodchikov (KZ), connection 58 79
Knizhnik — Zamolodchikov (KZ), equation 58 78
Knot 90
Kontsevich integral 133
Labelled tree 50
Lagrangian 1
Lagrangian, subbundle 6
Laplace operator 146
Laurent, polynomial 18
Level 26 29 43
Lickorish generators 114
Lie algebras, of loop groups 22
Lie algebras, of vector fields 2
Link 90
Link, colored 94
Linking number 91
Local horizontal moves 93 134
Logarithmic differential form 76
Loop algebra 14
Loop group 14
Mapping class group 90 112
Mapping torus 111
Marsden-Weinstein quotient 124
Matrix integral 162
Maurer-Cartan form 22
Mirror image 100
Mobius transformation 59
Modular transformation S matrix 71
Moduli space, of flat connections 124 161
Moduli space, surfaces 163
Moment map 124
Monodromy representation 80 87
Monodromy representation, universal expression of 132
Morse function 118
Multiple zeta value 137
Multiplicativity 9
Multiplicity of a representation 26
Newton's equation 1
Null vector 27
Operator product expansion (OPE) 64 65
Order m invariants 128
Order m invariants, for the pure braid group 134
Orientation axiom 9
Parallel translation 59
Partition function 8 42
Pentagon relation 86
Picard's iteration 131
Poisson, bracket 2
Polarization 6
Polarization, Kahler 6
Polyakov — Wiegmann formula 31
Polylogarithm 137
Primary, field 62 63
Primary, section 39
Projectively linear representation 115
Projectively linear representation, of the mapping class group 115
Pure braid group 75
Quantization 5
Quantization, canonical 6
Quantum, Clebsch — Gordan rule 49
Quantum, Hilbert space 9
Quantum, mechanics 4
Ray — Singer torsion 146
Real monoidal transformation 154
Regular singularities 84
Regularized determinant 146
Reidemeister torsion 147
Representations, of affme Lie algebras 26 38
Representations, of braid groups 80
Representations, of Lie algebras 23
Representations, of mapping class groups 110
Representations, of sfe(C) 24
Representations, of the gauge group 38
Ribbon graph 162
Riemann sphere 42
Schwarzian derivative 67
Secondary field 62
Sigma model 7
Signature of a link 105
Singular knots 128
Skein relation 95
Space of conformal blocks 44
Space of conformal blocks, dimension of 71 73
Space of conformal blocks, for a torus 69
Space of connections 121
Special conformal transformation 60
Spectral zeta function 146
Spin j representation 24
Stably equivalent 118
Stationary phase method 144
Sugawara operator 28
Symplectic, form 2
Symplectic, manifold 2
Tangle 101
Tangle, operator 102
Tensor product, of representations of a Lie algebra 25
Topological quantum field theory 110
Trefoil knot 101
Truncated polynomial ring 71
Universal enveloping algebra 24
Upper half plane 68
Vassiliev invariant 128
Vassiliev invariant, of order m 128
Verlinde, algebra 71
Verlinde, basis 70
Verlinde, formula 71
Verma module 24 27
Vertex operator 62
Virasoro Lie algebra 20 29
Volume form of SU(2) 29 122
Weight system 129 135
Wess — Zumino — Witten, action 29
Wess — Zumino — Witten, model 29
Wess — Zumino — Witten, term 30 123
Wilson line operator 125
Witten's invariant 108
Writhe 97
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