TY - JOUR
T1 - Gaudin models and bending flows: a geometrical point of view
JF - J. Phys. A: Math. Gen. 36 (2003) 11655-11676
Y1 - 2003
A1 - Gregorio Falqui
A1 - Fabio Musso
AB - 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.
PB - IOP Publishing
UR - http://hdl.handle.net/1963/2884
U1 - 1816
U2 - Mathematics
U3 - Mathematical Physics
ER -