Quantisation of bending flows

Nonlinear Sciences – Exactly Solvable and Integrable Systems

Scientific paper

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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.

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