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.

Talk given at the Alushta Conference,June 1994,preprint UUITP-16/94,29 p.,Latex file

References in corpus (5)

• Derivation of the Verlinde Formula from Chern-Simons Theory and the G/G model
• Integrable Systems for Particles with Internal Degrees of Freedom
• Classical R-matrix structure for the Calogero model
• $G/G$--Topological Field Theories by Cosetting $G_k$
• Degenerations of Sklyanin algebra and Askey-Wilson polynomials

Cited by in corpus (10)

• Gauge Theories and Macdonald Polynomials
• Bootstrapping the superconformal index with surface defects
• On Hamiltonian structure of the spin Ruijsenaars-Schneider model
• Trigonometric Sutherland systems and their Ruijsenaars duals from symplectic reduction
• Duality between the trigonometric BC(n) Sutherland system and a completed rational Ruijsenaars-Schneider-van Diejen system
• R-matrix Quantization of the Elliptic Ruijsenaars--Schneider model
• Global description of action-angle duality for a Poisson-Lie deformation of the trigonometric ${\mathrm{BC}}_n$ Sutherland system
• A note on the action-angle variables for the rational Calogero-Moser system
• Geometric construction of the classical $R$-matrices for the elliptic and trigonometric Calogero-Moser systems
• Integrable many-body systems of Calogero-Ruijsenaars type