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Integrable many-body systems in the field theories. (English) Zbl 0855.35106

Theor. Math. Phys. 103, No. 3, 681-700 (1995) and Teor. Mat. Fiz. 103, No. 3, 437-460 (1995).
Summary: We review recent results which clarify the role of the integrable many-body problems within 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.
The interpretation of the many-body dynamics as a motion on the different moduli spaces as well as the property of duality is discussed. A 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 group theory. The appearance of Calogero-type systems in different physical phenomena is mentioned.

MSC:

35Q40 PDEs in connection with quantum mechanics
37J35 Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
81V70 Many-body theory; quantum Hall effect
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