Comultiplication in ABCD algebra and scalar products of Bethe wave functions

TL;DR

This paper offers a new proof for the scalar products of Bethe wave functions in integrable models, using direct computation instead of previous recursive methods, enhancing understanding of algebraic structures in quantum integrability.

Contribution

It provides an alternative, direct computational proof for scalar products of Bethe wave functions, complementing earlier recursive approaches.

Findings

New proof based on direct computation

Clarifies algebraic structure of Bethe wave functions

Supports previous results with an alternative method

Abstract

The representation of scalar products of Bethe wave functions in terms of the Dual Fields, proven by A.G.Izergin and V.E.Korepin in 1987, plays an important role in the theory of completely integrable models. The proof in \cite{Izergin87} and \cite{Korepin87} is based on the explicit expression for the "senior" coefficient which was guessed in \cite{Izergin87} and then proven to satisfy some recurrent relations, which determine it unambiguously. In this paper we present an alternative proof based on the direct computation.