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Classical and Quantum \({\mathcal {W}}\)-Algebras and Applications to Hamiltonian Equations

  • Alberto De SoleEmail author
Chapter
First Online:
Part of the Springer INdAM Series book series (SINDAMS, volume 37)

Abstract

We start by giving an overview of the four fundamental physical theories, namely classical mechanics, quantum mechanics, classical field theory and quantum field theory, and the corresponding algebraic structures, namely Poisson algebras, associative algebras, Poisson vertex algebras and vertex algebras. We then focus on classical and quantum \(\mathcal {W}\)-algebras, with a particular emphasis on their application to integrable Hamiltonian PDE.

Keywords

Vertex algebras Classical \({\mathcal {W}}\)-algebras Hamiltonian reduction Integrable Hamiltonian systems 
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Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Rome La SapienzaRomaItaly

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