Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2006-10-03
Nonlinear Sciences
Exactly Solvable and Integrable Systems
7 pages, submitted to Czech. J. Phys
Scientific paper
10.1007/s10582-006-0415-9
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.
Falqui Gregorio
Musso Fabio
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