How to find the Lax pair from the Yang-Baxter equation. (English) Zbl 0742.58057
The authors give a brief description of the Yang-Baxter equations which play an important role in the theory of classical and quantum integrable systems. For a more fruitful application of the theory to the quantum case, a procedure for constructing the quantum Lax pair from the Yang- Baxter equations is required. By using an infinitesimal version of the Yang-Baxter equations, the authors describe an explicit procedure for constructing a quantum Lax pair. They illustrate their results by applying their procedure to study in some detail the Heisenberg XYZ model.
Reviewer: C.S.Sharma (London)
MSC:
| 58J50 | Spectral problems; spectral geometry; scattering theory on manifolds |
| 34L25 | Scattering theory, inverse scattering involving ordinary differential operators |
| 17B81 | Applications of Lie (super)algebras to physics, etc. |
| 35P25 | Scattering theory for PDEs |
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