Fermionic integrable models and graded Borchers triples

TL;DR

This paper constructs fermionic integrable quantum field models in 1+1 dimensions using operator algebra methods, introducing graded-local fields and confirming fermionic scattering states.

Contribution

It introduces a new operator-algebraic approach to fermionic integrable models via graded Borchers triples, expanding the framework of quantum field theory.

Findings

Construction of graded-local field algebras with fermionic scattering states

Verification of fermionic asymptotic particles using Haag-Ruelle theory

Application of existing nuclearity results to fermionic models

Abstract

We provide an operator-algebraic construction of integrable models of quantum field theory on 1+1 dimensional Minkowski space with fermionic scattering states. These are obtained by a grading of the wedge-local fields or, alternatively, of the underlying Borchers triple defining the theory. This leads to a net of graded-local field algebras, of which the even part can be considered observable, although it is lacking Haag duality. Importantly, the nuclearity condition implying nontriviality of the local field algebras is independent of the grading, so that existing results on this technical question can be utilized. Application of Haag-Ruelle scattering theory confirms that the asymptotic particles are indeed fermionic. We also discuss connections with the form factor programme.