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

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Kac V. — Vertex Algebras for Beginners

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Название: Vertex Algebras for Beginners

Автор: Kac V.

Аннотация:

An introduction to algebraic aspects of conformal field theory, for graduate students, research mathematicians, and physicists working in mathematical aspects of quantum field theory. Contains chapters on Wightman axioms and vertex algebras, calculus of formal distributions, local fields, structure theory of vertex algebras, and examples of vertex algebras and their applications. This second edition adds material and simplifies exposition.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 141

Добавлена в каталог: 04.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

-th product of fields      38 39
-th product of formal distributions      21
conformal superalgebra      130
superconformal vector      123
superconformal vertex algebra      123
vertex superalgebra      127
superconformal Lie algebra      126
superconformal vertex algebra      126
conformal superalgebra      131
-algebra      67
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 $\mathcal{D}$ of regular differential operators on $\mathbb{C}\backslash\{0\}$       98
Lie algebra $\widehat{gl}_{\infty}$       98
Lie algebra $\widetilde{gl}_{\infty}$       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
Neveu — Schwarz algebra      123
Neveu — Schwarz conformal superalgebra      129
Non-commutative Wick formula      70
Normally ordered product      37 42
Operator product expansion (OPE)      21
Orbifold model      68
Oscillator algebra      25
Parity      11 19
Pauli matrices      131
Poincar $\acute{e}$ 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
Two-cocycle      98 105
Two-cocycle of a conformal superalgebra      35
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
Weak locality      82
Weyl affinization      47
Wick theorem      42

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