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

November 07, 2011

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
can be naturally interpreted to represent particle productions.

Keywords:

2D QFT, wedge-local nets, interacting models