Construction of wedge-local nets of observables through Longo-Witten endomorphisms. II

TL;DR

This paper extends the construction of wedge-local nets of observables using Longo-Witten endomorphisms, focusing on the U(1)-current algebra and free massless fermionic nets to develop new interacting models with particle number mixing.

Contribution

It introduces new Longo-Witten endomorphisms on the U(1)-current net via restriction from fermionic nets, leading to novel interacting wedge-local models in two-dimensional spacetime.

Findings

Constructed new families of interacting wedge-local nets.

Developed endomorphisms that mix particle number sectors.

Produced models with non-trivial S-matrices that alter particle numbers.

Abstract

In the first part, we have constructed several families of interacting wedge-local nets of von Neumann algebras. In particular, there has been discovered a family of models based on the endomorphisms of the U(1)-current algebra of Longo-Witten. In this second part, we further investigate endomorphisms and interacting models. The key ingredient is the free massless fermionic net, which contains the U(1)-current net as the fixed point subnet with respect to the U(1) gauge action. Through the restriction to the subnet, we construct a new family of Longo-Witten endomorphisms on the U(1)-current net and accordingly interacting wedge-local nets in two-dimensional spacetime. The U(1)-current net admits the structure of particle numbers and the S-matrices of the models constructed here do mix the spaces with different particle numbers of the bosonic Fock space.