Vertex Algebras
Vacuum Field Identity
Creation Property
Annihilation Property
Vacuum Uniqueness
Translation Covariance
Derivative Relations
Translation of Vacuum
Infinitesimal Generators
Jacobi Identity Formulation
Locality of Fields
Commutator Relations
Mode-Level Locality
Consequences for Products
Axiom Compatibility
Independence Relations
Derived Properties
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3. Basic Structure of Vertex Algebras
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5. Core Operations and Concepts