Vertex Algebras

  1. Core Operations and Concepts
    1. Operator Product Expansion
      1. OPE Definition
        1. Singular Parts
          1. Regular Parts
            1. Pole Structure
              1. Residue Calculations
                1. OPE Coefficients
                2. Products of Operators
                  1. n-th Products
                    1. Product Formulas
                      1. Calculation Methods
                        1. Associativity Properties
                        2. Normal Ordering
                          1. Definition and Motivation
                            1. Normal Ordered Products
                              1. Wick's Theorem
                                1. Contraction Rules
                                  1. Applications to Free Fields
                                  2. Commutator Relations
                                    1. Mode Commutators
                                      1. Field Commutators
                                        1. Dong's Lemma
                                          1. Skew-Symmetry
                                            1. Borcherds Identity

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                                          4. Axioms and Fundamental Properties

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                                          6. Fundamental Examples