On the duality between the hyperbolic Sutherland and the rational Ruijsenaars-Schneider models

Details On the duality between the hyperbolic Sutherland and the rational Ruijsenaars-Schneider models On the duality between the hyperbolic Sutherland and the rational Ruijsenaars-Schneider models

2009-01-14

arxiv.org/abs/0901.1983v2

J. Phys. A: Math. Theor. 42 (2009) 185202

Physics

Mathematical Physics

16 pages, v2: comments and references added at the end of the text

Scientific paper

10.1088/1751-8113/42/18/185202

We consider two families of commuting Hamiltonians on the cotangent bundle of the group GL(n,C), and show that upon an appropriate single symplectic reduction they descend to the spectral invariants of the hyperbolic Sutherland and of the rational Ruijsenaars-Schneider Lax matrices, respectively. The duality symplectomorphism between these two integrable models, that was constructed by Ruijsenaars using direct methods, can be then interpreted geometrically simply as a gauge transformation connecting two cross sections of the orbits of the reduction group.

Affiliated with

Also associated with

No associations

Rating

On the duality between the hyperbolic Sutherland and the rational Ruijsenaars-Schneider models does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the duality between the hyperbolic Sutherland and the rational Ruijsenaars-Schneider models, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the duality between the hyperbolic Sutherland and the rational Ruijsenaars-Schneider models will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-375439