Integrable many-body problems from the field theories

TL;DR

This paper reviews how integrable many-body problems emerge from quantum field theories, highlighting their role in describing topological degrees of freedom, dualities, and connections to Calogero systems across physics.

Contribution

It clarifies the relationship between integrable many-body systems and quantum field theories, emphasizing their derivation from field theory structures and group-theoretic interpretations.

Findings

Many-body dynamics relate to moduli space motions

Duality properties are discussed in the context of these systems

Calogero-type systems appear in various physical phenomena

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.