Classical nonlinear σ models on Grassmann manifolds of compact or noncompact type

DOI10.1063/1.527723zbMath0644.58037OpenAlexW2004505255MaRDI QIDQ3787181

B. M. A. G. Piette, Jean-Pierre Antoine

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1063/1.527723

zbMATH Keywords

Bäcklund transformationEuclidean regimeGrassmannian \(\sigma \) models

Mathematics Subject Classification ID

Applications of global analysis to the sciences (58Z05) Global differential geometry (53C99) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

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Cites Work

• Bäcklund transformations for nonlinear sigma models with values in Riemannian symmetric spaces
• The soliton correlation matrix and the reduction problem for integrable systems
• Bäcklund transformations and soliton-type solutions for sigma models with values in real Grassmannian spaces
• Classical solutions of two-dimensional Grassmannian models
• Local theory of solutions for the \(0(2k+1)\sigma\)-model
• Integration of nonlinear equations of mathematical physics by the method of inverse scattering. II
• Integrable Hamiltonian systems and interactions through quadratic constraints
• Pseudo-Hermitian symmetric spaces
• Explicit forms of Bäcklund transformations for the Grassmannian and C P N−1 sigma models
• Infinite-dimensional Lie algebras acting on the solution space of various σ models
• Gauge equivalence of sigma models with non-compact Grassmannian manifolds