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Equivalence of two graphical calculi. (English) Zbl 0784.53056
Summary: We consider the integrable systems which are connected with separation of variables in the Helmholtz operator on the real Riemannian spaces of constant curvature. An isomorphism is given for these systems with a quantum hyperbolic Gaudin magnet. Using this isomorphism, the complete classification of all separable coordinate systems on the manifolds considered is provided by means of the corresponding L-operators for the Gaudin magnet.
MSC:
53Z05Applications of differential geometry to physics
81V10Electromagnetic interaction; quantum electrodynamics