An integrable BC(n) Sutherland model with two types of particles

TL;DR

This paper derives an integrable hyperbolic BC(n) Sutherland model with two particle types on the half-line using Hamiltonian reduction, establishing its integrability and providing a solution construction algorithm.

Contribution

It introduces a new integrable BC(n) Sutherland model with two particle types derived via Hamiltonian reduction of SU(n,n).

Findings

Model is proven integrable.

Provides a simple solution construction algorithm.

Characterizes interactions with three coupling constants.

Abstract

A hyperbolic BC(n) Sutherland model involving three independent coupling constants that characterize the interactions of two types of particles moving on the half-line is derived by Hamiltonian reduction of the free geodesic motion on the group SU(n,n). The symmetry group underlying the reduction is provided by the direct product of the fixed point subgroups of two commuting involutions of SU(n,n). The derivation implies the integrability of the model and yields a simple algorithm for constructing its solutions.