## Axioms for a vertex algebra and the locality of quantum fields |

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### Contents

Axioms for a vertex algebra | 35 |

B Analytic method | 95 |

List of expansions of x yry zQx zp | 101 |

Copyright | |

1 other sections not shown

### Common terms and phrases

admissible fields Ae(z affine Lie algebra associative algebra bilinear map binary operations central charge conformal field theory conformal vector conformal vertex algebra consider Corollary defined Definition denote endomorphism existence theorem exists a unique field A(z finitely many terms g-module graded vertex algebra Griess algebra Hence homomorphism of vertex invariant bilinear form isomorphism Jacobi identity Lemma Let A(z Lie algebra structure Lie bracket linear map s\v mutually local fields nonnegative integer nonzero vector normally ordered product Note notion operator product expansion pairwise mutually Proof Proposition quantum operator algebra quasiconformal vertex algebra quotient space satisfies L1)-(L3 scalar series A(z skew symmetry space of fields st product State-field correspondence Subsection sufficiently large suppose given symmetric tensor product theory of vertex translation covariant unique vertex algebra V/TV vacuum vector Verma module Vertex algebra associated vertex algebra structure vertex operator algebras Virasoro algebra weak module Z2-graded vector space