TY - JOUR
T1 - Quantisation of bending flows
JF - Czechoslovak Journal of Physics 56 (2006), n. 10-11, 1143-1148
Y1 - 2006
A1 - Gregorio Falqui
A1 - Fabio Musso
AB - We 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.
UR - http://hdl.handle.net/1963/2537
U1 - 1582
U2 - Mathematics
U3 - Mathematical Physics
ER -
TY - RPRT
T1 - On Separation of Variables for Homogeneous SL(r) Gaudin Systems
Y1 - 2006
A1 - Gregorio Falqui
A1 - Fabio Musso
AB - By 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.
JF - Math. Phys. Anal. Geom. 9 (2006), n. 3, 233-262 (2007)
UR - http://hdl.handle.net/1963/2538
U1 - 1581
U2 - Mathematics
U3 - Mathematical Physics
ER -
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 -