An Algebraic Approach to Form Factors

TL;DR

This paper introduces an algebraic framework that encodes form factor axioms in integrable quantum field theories, providing a systematic way to identify physically relevant representations and deriving universal eigenvalue formulas for conserved charges.

Contribution

It develops an associative algebra incorporating form factor axioms, offering a new algebraic method to select correct representations in integrable QFTs.

Findings

Algebraic structure implements form factor axioms

Universal formula for eigenvalues of conserved charges

Provides a systematic selection of representations

Abstract

An associative $*$-algebra is introduced (containing a $TTR$-algebra as a subalgebra) that implements the form factor axioms, and hence indirectly the Wightman axioms, in the following sense: Each $T$-invariant linear functional over the algebra automatically satisfies all the form factor axioms. It is argued that this answers the question (posed in the functional Bethe ansatz) how to select the dynamically correct representations of the $TTR$-algebra. Applied to the case of integrable QFTs with diagonal factorized scattering theory a universal formula for the eigenvalues of the conserved charges emerges.