Kac V. — Vertex Algebra for Beginners :: Электронная библиотека попечительского совета мехмата МГУ

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Kac V. — Vertex Algebra for Beginners

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Название: Vertex Algebra for Beginners

Автор: Kac V.

Аннотация:

This is a revised and expanded edition of Kac's original introduction to algebraic aspects of conformal field theory, which was published by the AMS in 1996. The volume serves as an introduction to algebraic aspects of conformal field theory, which in the past 15 years revealed a variety of unusual mathematical notions. Vertex algebra theory provides an effective tool to study them in a unified way.
In the book, a mathematician encounters new algebraic structures that originated from Einstein's special relativity postulate and Heisenberg's uncertainty principle. A physicist will find familiar notions presented in a more rigorous and systematic way, possibly leading to a better understanding of foundations of quantum physics.

Язык:

Рубрика: Математика/Алгебра/Теория представлений/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 141

Добавлена в каталог: 26.03.2005

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Предметный указатель

2-cocycle      98 105
2-cocycle of a conformal superalgebra      35
Affine central charge      48
Affine Kac-Moody algebra      26
Affine vertex algebra      76
Affinization      26
Affinization of a vertex algebra      61
Associative superalgebra      18
Automorphism of a vertex algebra      60
Borcherds commutator formula      66
Borcherds identity      71
Borcherds OPE formula      64
Boson-fermion correspondence      93
Bosonization      88
Bracket      19
Casimir operator      116
Causal order      3
Central charge      31 79
CHARACTER      89
Charge      88
Charge decomposition      89
Charge operator      88
Charged free fermions      28 87 108
Chiral algebra      9
Clifford affinization      27
Conformal group      5
Conformal quantum field theory      5
Conformal superalgebra      33
Conformal vector      79
Conformal vertex algebra      79
Conformal weight      28 80 130
Coset model      67
Current algebra      26
Current conformal algebra      36
Currents      26
Dedekind $\eta$ -function      90
Derivation of a vertex algebra      60
Dong’s lemma      40
Dual bases      48
Dual Coxeter number      117
Eigendistribution      28
Energy      89
Energy operator      89
Energy-momentum field      79
Existence theorem      62
Field      12 37 38
Field algebra      82
Field representation      45
Formal delta-function      15
Formal distribution      15
Forward cone      3
Free boson      25 48
Free bosonic vertex algebra      70
Free fermionic vertex algebra      70
Free fermions      52
Free field theory      43
Free neutral fermion      27
Frenkel — Kac construction      113
General linear field algebra      41
Generating set of fields      63
Goddard uniqueness theorem      61
Goddard — Kent — Olive construction      120
Graded conformal superalgebra      130
Graded Lie superalgebra of formal distributions      46
Graded vertex algebra      72
Group $GL_{\infty}$       95
Hamiltonian      28 72
Holomorphic vertex algebra      13
Homomorphism of vertex algebras      59
Ideal of a vertex algebra      60
Induced module      45
Infinitesimal translation operator      12 57
Inner automorphism of a vertex algebra      75
Integral lattice      101
Integration by parts      15
Invariant bilinear form      26
Jacobi triple product identity      90
Kac — Todorov model      124
KP hierarchy      95 96
Lattice vertex algebra      101 106
Lie algebra $gl_{\infty}$       93

Lie algebra $\hat{gl}_{\infty}$       98
Lie algebra $\mathcal{D}$ of regular differential operators on $\mathbb{C}\ {0}$       98
Lie algebra $\tilde{gl}_{\infty}$       97
Lie superalgebra      19
Lie superalgebra of formal distributions      31 45
Light cone coordinates      6
Linear field algebra      41
Local linear field algebra      41
Locality      19
Locality axiom      12 57
Minkowski space-time      3
Mobius-conformal vertex algebra      76
Mutually local formal distributions      19
N = 1 superconformal vector      123
N = 1 superconformal vertex algebra      123
N = 1 vertex superalgebra      127
N = 2 conformal superalgebra      130
N = 2 superconformal Lie algebra      126
N = 2 superconformal vertex algebra      126
N = 4 conformal superalgebra      131
n-th product of fields      38 39
n-th product of formal distributions      21
Neveu — Schwarz algebra      123
Neveu — Schwarz conformal superalgebra      129
Normally ordered product      37 42
Operator product expansion (OPE)      21
Orbifold model      68
Oscillator algebra      25
Parity      11 19
Pauli matrices      131
Poincare group      3
Positive and negative parts of a formal distribution      19
Primary field      80
Quantum field theory      3
Quasiprimary field      76
Quasisymmetry      58
Regular Lie superalgebra of formal distributions      68
Residue      15
Restricted representation      46
Root lattice      111
Root system      111
Singular vector      47
Skew-supersymmetric bilinear form      27
Space of states      12
Space-like separated subsets      3
State-field correspondence      12
Strongly generating set of fields      63
Subalgebra of a vertex algebra      59
Sugawara construction      118
Superaffine vertex algebra      76
Superaffinization      26
Superconformal Lie algebra      125
Supercurrent      27
Supercurrent algebra      69
Superdimension      12
Superfields      127
Superspace      11
Supersymmetric bilinear form      26
Taylor’s Formula      24 39
Tensor product of vertex algebras      60
Translation covariance axiom      12 57
Twisted group algebra      104
Universal affine vertex algebra      70
Universal vertex algebra associated to a regular Lie superalgebra of formal distributions      69
Vacuum axiom      12 57
Vacuum subalgebra      63
Vacuum vector      12
Veneziano field      92
Verma module      46
Vertex algebra      12 57
Vertex algebra $W_{1+\infty,c}$       100
Vertex operator      10 92 108
Virasoro algebra      30
Virasoro conformal algebra      36
Virasoro field      79
Virasoro formal distribution      31
W-algebra      67
Weak locality      82
Weyl amnization      47
Wick theorem      42
“Non-commutative” Wick formula      70

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