%0 Journal Article
%J Czechoslovak Journal of Physics 56 (2006), n. 10-11, 1143-1148
%D 2006
%T Quantisation of bending flows
%A Gregorio Falqui
%A Fabio Musso
%X 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.
%B Czechoslovak Journal of Physics 56 (2006), n. 10-11, 1143-1148
%G en_US
%U http://hdl.handle.net/1963/2537
%1 1582
%2 Mathematics
%3 Mathematical Physics
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-12-19T10:53:01Z\\nNo. of bitstreams: 1\\n0610003v1.pdf: 113471 bytes, checksum: 34a8a67eda45bff5d2e70aaa0c1edf65 (MD5)
%R 10.1007/s10582-006-0415-9
%0 Report
%D 2006
%T On Separation of Variables for Homogeneous SL(r) Gaudin Systems
%A Gregorio Falqui
%A Fabio Musso
%X 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.
%B Math. Phys. Anal. Geom. 9 (2006), n. 3, 233-262 (2007)
%G en_US
%U http://hdl.handle.net/1963/2538
%1 1581
%2 Mathematics
%3 Mathematical Physics
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2007-12-19T11:26:08Z\\nNo. of bitstreams: 1\\n0402026v1.pdf: 312976 bytes, checksum: e99c241d72908de5b5bf69b0a7dd1c5c (MD5)
%R 10.1007/s11040-006-9012-1
%0 Journal Article
%J J. Phys. A: Math. Gen. 36 (2003) 11655-11676
%D 2003
%T Gaudin models and bending flows: a geometrical point of view
%A Gregorio Falqui
%A Fabio Musso
%X 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.
%B J. Phys. A: Math. Gen. 36 (2003) 11655-11676
%I IOP Publishing
%G en_US
%U http://hdl.handle.net/1963/2884
%1 1816
%2 Mathematics
%3 Mathematical Physics
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-09-10T09:56:34Z\\nNo. of bitstreams: 1\\n0306005v1.pdf: 262369 bytes, checksum: 4563b661b4ec9bfabee142962f7d9279 (MD5)
%R 10.1088/0305-4470/36/46/009