1999/06/21 by Bani Mitra Sodermark, Sodermark, Bani Mitra
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #hep-th
paper · pdf · doi:10.48550/arxiv.hep-th/9906159
29 pages, 1 figure, review article, LaTeX
arxiv created 1999/06/21 · openalex publication_date 1999/06/21 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A pedagogical presentation of integrable models with special reference to the Toda lattice hierarchy has been attempted. The example of the KdV equation has been studied in detail, beginning with the infinite conserved quantities and going on to the Lax formalism for the same. We then go on to symplectic manifolds for which we construct the Lax operator. This formalism is applied to Toda Lattice systems. The Zakharov Shabat formalism aimed at encompassing all integrable models is also covered after which the zero curvature condition and its fallout are discussed. We then take up Toda Field Theories and their connection to W algebras via the Hamiltonian reduction of the WZNW model. Finally, we dwell on the connection between four dimensional Yang Mills theories and the KdV equation along with a generalization to supersymmetry.