On the Existence of Local Observables in Theories With a Factorizing S-Matrix

TL;DR

This paper verifies a criterion for local quantum fields with factorizing scattering matrices in a specific model, providing a new constructive approach to quantum field theory through nuclearity analysis of Fermionic Fock spaces.

Contribution

It demonstrates the existence of local observables in a non-trivial model with a factorizing S-matrix, advancing constructive quantum field theory methods.

Findings

Verified a criterion for local quantum fields in a specific model

Established a new constructive approach to quantum field theory

Analyzed nuclearity properties of Fermionic Fock spaces

Abstract

A recently proposed criterion for the existence of local quantum fields with a prescribed factorizing scattering matrix is verified in a non-trivial model, thereby establishing a new constructive approach to quantum field theory in a particular example. The existence proof is accomplished by analyzing nuclearity properties of certain specific subsets of Fermionic Fock spaces.