Infinite-dimensional Lie algebras acting on the solution space of various σ models

DOI10.1063/1.527736zbMath0639.58036OpenAlexW2043488859MaRDI QIDQ3780166

Yvan Saint-Aubin, Michel Jacques

Publication date: 1987

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.527736

zbMATH Keywords

Infinite-dimensional Lie algebras of infinitesimal transformations

Mathematics Subject Classification ID

Applications of global analysis to the sciences (58Z05) Lie algebras and Lie superalgebras (17B99)

Related Items (8)

Classical nonlinear σ models on Grassmann manifolds of compact or noncompact type ⋮ Collapse and exponentiation of infinite symmetry algebras of Euclidean projective and Grassmannian σ models ⋮ Explicit solutions of Grassmannian σ models ⋮ Actions of Loop Groups on Harmonic Maps ⋮ The ADHM construction and non-local symmetries of the self-dual Yang-Mills equations ⋮ Hierarchy structure in integrable systems of gauge fields and underlying Lie algebras ⋮ Integrated Lax formalism for principal chiral model ⋮ Description of surfaces associated with Grassmannian sigma models on Minkowski space

Cites Work

• Solitons and infinite dimensional Lie algebras
• Bäcklund transformations for nonlinear sigma models with values in Riemannian symmetric spaces
• Non-Abelian bosonization in two dimensions
• Classical and quantum algebras of non-local charges in \(\sigma\) models
• Infinite dimensional Lie algebras acting on chiral fields and the Riemann-Hilbert problem
• The soliton correlation matrix and the reduction problem for integrable systems
• A new approach to the self-dual Yang-Mills equations
• The reduction problem and the inverse scattering method
• Integrable Hamiltonian systems and interactions through quadratic constraints
• Formal power series solutions of supersymmetric (N=3) Yang–Mills equations

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