You are here

Gaudin models and bending flows: a geometrical point of view

TitleGaudin models and bending flows: a geometrical point of view
Publication TypeJournal Article
Year of Publication2003
AuthorsFalqui, G, Musso, F
JournalJ. Phys. A: Math. Gen. 36 (2003) 11655-11676

In this paper we discuss the bihamiltonian formulation of the (rational XXX) Gaudin models of spin-spin interaction, generalized to the case of sl(r)-valued spins. In particular, we focus on the homogeneous models. We find a pencil of Poisson brackets that recursively define a complete set of integrals of the motion, alternative to the set of integrals associated with the \\\'standard\\\' Lax representation of the Gaudin model. These integrals, in the case of su(2), coincide wih the Hamiltonians of the \\\'bending flows\\\' in the moduli space of polygons in Euclidean space introduced by Kapovich and Millson. We finally address the problem of separability of these flows and explicitly find separation coordinates and separation relations for the r=2 case.


Sign in