String Theory and Integrable Systems

Details String Theory and Integrable Systems String Theory and Integrable Systems

1993-10-18

arxiv.org/abs/hep-th/9310113v3

Physics

High Energy Physics

High Energy Physics - Theory

(to appear in "Mathematical Physics Towards the XXIst Century", Proc. Int. Conf. in Beer Sheva, March 1993), LaTeX, 25 pages,

Scientific paper

This is mainly a brief review of some key achievements in a `hot'' area of theoretical and mathematical physics. The principal aim is to outline the basic structures underlying {\em integrable} quantum field theory models with {\em infinite-dimensional} symmetry groups which display a radically new type of {\em quantum group} symmetries. Certain particular aspects are elaborated upon with some detail: integrable systems of Kadomtsev-Petviashvili type and their reductions appearing in matrix models of strings; Hamiltonian approach to Lie-Poisson symmetries; quantum field theory approach to two-dimensional relativistic integrable models with dynamically broken conformal invariance. All field-theoretic models in question are of primary relevance to diverse branches of physics ranging from nonlinear hydrodynamics to string theory of fundamental particle interactions at ultra-high energies.

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