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Physics of Atomic Nuclei

A quantum version of the inverse scattering transformation

Frank Göhmann, V. E. Korepin

Published Jun 1, 2002• 3 citations
Publisher

Abstract

We derive a formula that expresses the local spin and field operators of fundamental graded models in terms of the elements of the monodromy matrix. This formula may be understood as a quantum version of the classical inverse scattering transformation.
DOI
10.1134/1.1490094

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For the integrable spin- s XXZ chain we express explicitly any given spin- s form factor in terms of a sum over the scalar products of the spin-1/2 fundamental operators of the algebraic Bethe ansatz. Here, they are given by the operator-valued matrix elements of the monodromy matrix of the spin-1/2 XXZ spin chain. We derive the reduction formula of higher-spin form factors by the fusion method in detail. We call an arbitrary matrix element of a local operator between two Bethe eigenstates a form factor of the operator in this paper. We thus revise the derivation of the higher-spin XXZ form factors given in a previous paper. The revised method has several interesting applications in mathematical physics. For instance, we express the spin- s XXZ correlation function of an arbitrary entry at zero temperature in terms of a sum of multiple integrals.