On the equivalence theorem for integrable systems

TL;DR

This paper examines the invariance of the S-matrix under field transformations in integrable systems, specifically analyzing the Alday-Arutyunov-Frolov model to demonstrate how different formulations relate through the equivalence theorem.

Contribution

It provides a detailed analysis of the equivalence theorem for integrable systems using two formulations of the Alday-Arutyunov-Frolov model, including the invariance of the S-matrix and Hamiltonian diagonalization methods.

Findings

S-matrix remains invariant under field transformations

Field transformation simplifies Dirac brackets to standard commutation relations

Method for diagonalizing the transformed Hamiltonian via self-adjoint extensions

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.