Riemann surfaces, separation of variables and classical and quantum integrability

Abstract

We show that Riemann surfaces, and separated variables immediately provide classical Poisson commuting Hamiltonians. We show that Baxter's equations for separated variables immediately provide quantum commuting Hamiltonians. The construction is simple, general, and does not rely on the Yang--Baxter equation.

10 pages. Fixed a typo, added a reference

References in corpus (1)

• The symplectic structure of rational Lax pair systems

Cited by in corpus (7)

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• Quantum discrete Dubrovin equations