Vertex Algebras

  1. Fundamental Examples
    1. Commutative Vertex Algebras
      1. Definition and Structure
        1. Polynomial Algebras
          1. Trivial OPE Structure
            1. Simple Examples
            2. Heisenberg Vertex Algebra
              1. The Heisenberg Lie Algebra
                1. Canonical Commutation Relations
                  1. Central Extension
                    1. Generators and Structure
                    2. Fock Space Construction
                      1. Vacuum Vector
                        1. Creation Operators
                          1. Annihilation Operators
                            1. Fock Space Basis
                            2. Vertex Operator Realization
                              1. Explicit Vertex Operators
                                1. Mode Expansions
                                  1. OPE Calculations
                                    1. Normal Ordering Relations
                                  2. Lattice Vertex Algebras
                                    1. Even Lattice Theory
                                      1. Lattice Definitions
                                        1. Bilinear Forms
                                          1. Root Systems
                                            1. Lattice Automorphisms
                                            2. Vertex Operator Construction
                                              1. Lattice Vertex Operators
                                                1. Cocycle Factors
                                                  1. Twisted Group Algebra
                                                    1. State-Field Correspondence
                                                    2. Examples of Lattice Algebras
                                                      1. Root Lattice Constructions
                                                        1. Weight Lattice Cases
                                                          1. Exceptional Lattices

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                                                      5. Core Operations and Concepts

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                                                      7. Affine Vertex Algebras