00738nas a2200109   4500008004300000245003400043210003400077520044300111100002100554700001700575856003600592       2006                        en_Ud  00aQuantisation of bending flows0 aQuantisation of bending flows3 aWe briefly review the Kapovich-Millson notion of Bending flows as an integrable system on the space of polygons in ${\\\\bf R}^3$, its connection with a specific Gaudin XXX system, as well as the generalisation to $su(r), r>2$. Then we consider the quantisation problem of the set of Hamiltonians pertaining to the problem, quite naturally called Bending Hamiltonians, and prove that their commutativity is preserved at the quantum level.1 aFalqui, Gregorio1 aMusso, Fabio  uhttp://hdl.handle.net/1963/253700519nas a2200109   4500008004300000245006800043210006300111520016100174100002100335700001700356856003600373       2006                        en_Ud  00aOn Separation of Variables for Homogeneous SL(r) Gaudin Systems0 aSeparation of Variables for Homogeneous SLr Gaudin Systems3 aBy means of a recently introduced bihamiltonian structure for the homogeneous Gaudin models, we find a new set of Separation Coordinates for the sl(r) case.1 aFalqui, Gregorio1 aMusso, Fabio  uhttp://hdl.handle.net/1963/253801156nas a2200121   4500008004300000245006500043210006400108260001900172520076900191100002100960700001700981856003600998       2003                        en_Ud  00aGaudin models and bending flows: a geometrical point of view0 aGaudin models and bending flows a geometrical point of view  bIOP Publishing3 aIn 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.1 aFalqui, Gregorio1 aMusso, Fabio  uhttp://hdl.handle.net/1963/2884