标题： 通过Longo-Witten内自同态构造楔形局部观测算子网。 II 显示英文标题

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

摘要： 在第一部分中，我们构造了几个相互作用的楔形局部冯诺依曼代数网族。特别是，发现了一个基于Longo-Witten U(1)电流代数的自同态的模型族。在第二部分中，我们进一步研究自同态和相互作用模型。关键要素是自由无质量费米子网，它包含U(1)电流网作为相对于U(1)规范作用的固定子网。通过限制到子网，我们在U(1)电流网上构造了一类新的Longo-Witten自同态，并相应地在二维时空构造了相互作用的楔形局部网。U(1)电流网具有粒子数结构，这里构造的模型的S矩阵会混合玻色福克空间中不同粒子数的空间。 显示英文摘要

摘要： 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.