Diffeomorphism algebras and the Nahm and Ward equations

DOI10.1063/1.529918zbMath0744.58074OpenAlexW2091974828MaRDI QIDQ3991692

Sarbarish Chakravarty, Ezra T. Newman, Steven L. Kent

Publication date: 28 June 1992

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

Full work available at URL: https://doi.org/10.1063/1.529918

zbMATH Keywords

Liouville equationsToda latticeincompressible Euler equationsdiffeomorphism groupstranslational symmetriesmembrane equationsNahm's equationWard's equationanti-self-dual Yang-Mills equationsHeisenberg spin-chain equations

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Yang-Mills and other gauge theories in quantum field theory (81T13) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Infinite-dimensional Lie (super)algebras (17B65) NLS equations (nonlinear Schrödinger equations) (35Q55) Applications of PDEs on manifolds (58J90)

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Some reductions of the self-dual Yang–Mills equations to integrable systems in 2+1 dimensions, Lax pairs of integrable equations in \(1\leq d\leq 3\) dimensions as reductions of the Lax pair for the self-dual Yang-Mills equations

Cites Work

• A connection between the Einstein and Yang-Mills equations
• High symmetry solutions of the anti-self-dual Yang–Mills equations
• Integrable and solvable systems, and relations among them
• Integrable and chaotic motions of four vortices. I. The case of identical vortices
• Reductions of self-dual Yang-Mills fields and classical systems
• Geometric phase in the classical continuous antiferromagnetic Heisenberg spin chain