Vertex algebras for beginners
Vertex algebras for beginners
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DOI：
10.1090/ulect/010
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发表时间：
1997
期刊：
影响因子：
--
通讯作者：
V. Kac
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文献类型：
--
作者：
V. Kac
序言。第1章怀特曼公理和顶点代数1.1量子场论的怀特曼公理1.2：d = 2 QFT和手征代数。1.3顶点代数的定义1.4：全纯顶点代数。2：形式分布的微积分。2.1：正式的delta函数。2.2：形式分布a（z，w）的扩展。2.3：地点。2.4泰勒公式2.5当前代数。2.6共形权和Virasoro代数。2.7形式分布的李超代数和共形超代数。3、地方性。3.1：正常订购的产品。3.2：Dong's lemma. 3.3威克定理和一个“非交换”的推广。3.4形式分布的李超代数的限制和场表示。3.5：自由（超级）胸部。3.5：自由（超）费米子。4：顶点代数的结构理论。4.1：平移协方差的后果。4.2：拟对称。4.3超代数、理想和张量积4.4：唯一性定理。4.5存在定理。4.6：Borcherds OPE公式。4.7与形式分布的李超代数相关的顶点代数。4.8：Borcherds恒等式。4.9分次和Mobius共形顶点代数。4.10共形顶点代数。4.11域代数。5.顶点代数的例子及其应用。5.1：带电的自由费米子。5.2玻色子-费米子对应和KP层次。5.3：gl和W. 5.4格点代数5.5：简单格顶点代数。5.6根格顶点代数和仿射顶点代数。5.7仿射顶点代数的共形结构。5.8：超共形顶点代数。5.9关于共形超代数的分类。参考书目。指数
Preface. 1: Wightman axioms and vertex algebras. 1.1: Wightman axioms of a QFT. 1.2: d = 2 QFT and chiral algebras. 1.3: Definition of a vertex algebra. 1.4: Holomorphic vertex algebras. 2: Calculus of formal distributions. 2.1: Formal delta-function. 2.2: An expansion of a formal distribution a(z,w). 2.3: Locality. 2.4: Taylor's formula. 2.5: Current algebras. 2.6: Conformal weight and the Virasoro algebra. 2.7: Lie superalgebras of formal distributions and conformal superalgebras. 3: Local fields. 3.1: Normally ordered product. 3.2: Dong's lemma. 3.3: Wick's theorem and a "non-commutative" generalization. 3.4: Restricted and field representations of Lie superalgebras of formal distributions. 3.5: Free (super)bosoms. 3.5: Free (super)fermions. 4: Structure theory of vertex algebras. 4.1: Consequences of translation covariance. 4.2: Quasisymmetry. 4.3: Superalgebras, ideals, and tensor products. 4.4: Uniqueness theorem. 4.5: Existence theorem. 4.6: Borcherds OPE formula. 4.7: Vertex algebras associated to Lie superalgebras of formal distributions. 4.8: Borcherds identity. 4.9: Graded and Mobius conformal vertex algebras. 4.10: Conformal vertex algebras. 4.11: Field algebras. 5: Examples of vertex algebras and their applications. 5.1: Charged free fermions. 5.2: Boson-fermion correspondence and KP hierarchy. 5.3: gl and W. 5.4: Lattice vertex algebras. 5.5: Simple lattice vertex algebras. 5.6: Root lattice vertex algebras and affine vertex algebras. 5.7: Conformal structure for affine vertex algebras. 5.8: Superconformal vertex algebras. 5.9: On classification of conformal superalgebras. Bibliography. Index