On the derivation of Darboux form for the action-angle dual of trigonometric BC(n) Sutherland system

TL;DR

This paper verifies the canonical Poisson brackets of the action-angle dual of the trigonometric BC(n) Sutherland system using Hamiltonian reduction, complementing previous hyperbolic case studies.

Contribution

It provides a reduction-based calculation confirming the Darboux form for the dual system's phase space, extending prior work on hyperbolic models.

Findings

Confirmed canonical Poisson bracket relations for the dual system.

Extended the hyperbolic case analysis to the trigonometric BC(n) Sutherland system.

Validated the Darboux form for the dual model's phase space.

Abstract

Recently Feher and the author have constructed the action-angle dual of the trigonometric BC(n) Sutherland system via Hamiltonian reduction. In this paper a reduction-based calculation is carried out to verify canonical Poisson bracket relations on the phase space of this dual model. Hence the material serves complementary purposes whilst it can also be regarded as a suitable modification of the hyperbolic case previously sorted out by Pusztai.