Integrable many-body problems from the field theories

Abstract

We review recent results which clarify the role of the integrable many-body problems in the quantum field theory framework.They describe the dynamics of the topological degrees of freedom in the theories which are obtained by perturbing the topological ones by the proper Hamiltonians and sources. Interpretation of the many-body dynamics as a motion on the different moduli spaces as well as the property of duality is discussed.Tower of many-body systems can be derived from a tower of the field theories with appropriate phase spaces which have a transparent interpretation in terms of the group theory.The appearance of Calogero-type systems in different physical phenomena is mentioned.