Vertex Algebras

  1. Axioms and Fundamental Properties
    1. The Vacuum Axiom
      1. Vacuum Field Identity
        1. Creation Property
          1. Annihilation Property
            1. Vacuum Uniqueness
            2. The Translation Axiom
              1. Translation Covariance
                1. Derivative Relations
                  1. Translation of Vacuum
                    1. Infinitesimal Generators
                    2. The Locality Axiom
                      1. Jacobi Identity Formulation
                        1. Locality of Fields
                          1. Commutator Relations
                            1. Mode-Level Locality
                              1. Consequences for Products
                              2. Consistency Conditions
                                1. Axiom Compatibility
                                  1. Independence Relations
                                    1. Derived Properties

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                                  3. Basic Structure of Vertex Algebras

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                                  5. Core Operations and Concepts