On the equivalence theorem for integrable systems

Abstract

We investigate the equivalence theorem for integrable systems using two formulations of the Alday-Arutyunov-Frolov model. We show that the S-matrix is invariant under the field transformation which reduces the non-linear Dirac brackets of one formulation into the standard commutation relations in the second formulation. We also explain how to perform the direct diagonalization of the transformed Hamiltonian by constructing the states corresponding to self-adjoint extensions.

27 pages

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• TTbar deformation and the light-cone gauge
• On the quantization of continuous non-ultralocal integrable systems
• The Lax pair for the fermionic Bazhanov-Stroganov $R$-operator
• The tetrahedral Zamolodchikov algebra for the fermionic Bazhanov-Stroganov R-operator
• Exceptional solutions to the eight-vertex model and integrability of anisotropic extensions of massive fermionic models
• On extension of the Yang-Baxter equation and the fermionic $R$-operator
• On quantum Freidel-Maillet algebra for non-ultralocal integrable systems