Hidden geometrical structures in integrable models
نویسنده
چکیده
The bootstrap equations for the ADE series of purely elastic scattering theories have turned out to be intimately connected with the geometry of root systems and the Coxeter element. An informal review of some of this material is given, mentioning also a couple of other contexts – the Pasquier models, and the simply-laced affine Toda field theories – where similar structures are encountered. The relevance of twisted Coxeter elements is indicated, and a construction of these elements inspired by the twisted foldings of the affine Toda models is described.
منابع مشابه
Towards a Theory of Differential Constraints of a Hydrodynamic Hierarchy
We present a theory of compatible differential constraints of a hydrodynamic hierarchy of infinite-dimensional systems. It provides a convenient point of view for studying and formulating integrability properties and it reveals some hidden structures of the theory of integrable systems. Illustrative examples and new integrable models are exhibited.
متن کاملExamples of Integrable and Non-integrable Systems on Singular Symplectic Manifolds
We present a collection of examples borrowed from celestial mechanics and projective dynamics. In these examples symplectic structures with singularities arise naturally from regularization transformations, Appell’s transformation or classical changes like McGehee coordinates, which end up blowing up the symplectic structure or lowering its rank at certain points. The resulting geometrical stru...
متن کاملModelling of Random Geometrical Imperfections and Reliability Calculations for Thin Cylindrical Shell Subjected to Lateral Pressure
It is well known that it is very difficult to manufacture perfect thin cylindrical shell. Initial geometrical imperfections existing in the shell structure is one of the main determining factor for load bearing capacity of thin cylindrical shell under uniform lateral pressure. As these imperfections are random, the strength of same size cylindrical shell will also random and a statistical metho...
متن کاملComparison and evaluation of the performance of data-driven models for estimating suspended sediment downstream of Doroodzan Dam
Dams control most of the sediment entering the reservoir by creating static environments. However, sediment leaving the dam depends on various factors such as dam management method, inlet sediment, water height in the reservoir, the shape of the reservoir, and discharge flow. In this research, the amount of suspended sediment of Doroodzan Dam based on a statistical period of 25 years has been i...
متن کاملZamolodchikov’s Tetrahedron Equation and Hidden Structure of Quantum Groups
The tetrahedron equation is a three-dimensional generalization of the Yang-Baxter equation. Its solutions define integrable three-dimensional lattice models of statistical mechanics and quantum field theory. Their integrability is not related to the size of the lattice, therefore the same solution of the tetrahedron equation defines different integrable models for different finite periodic cubi...
متن کامل