用Longo-Witten自同态构造楔形局部观测网
Construction of wedge-local nets of observables through Longo-Witten endomorphisms
摘要：
Buchholz建立了一个处理无质量二维散射理论的方便框架。在这个框架下，我们证明了在渐近完备性和标准假设下，渐近代数和散射矩阵完全刻画了给定理论。然后，我们得到了几个家庭的相互作用的楔形局部网由一个纯粹的冯诺依曼代数过程。其中一个特殊的例子与Buchholz-Lechner-Summers的手征CFT的形变相吻合。在另一种情况下，我们设法完全确定严格的本地元素。最后，利用U（1）-流网和自由费米子网上的Longo-Witten自同态，构造了一大类楔形局域网.
英文摘要：
A convenient framework to treat massless two-dimensional scattering theories has been established by Buchholz. In this framework, we show that the asymptotic algebra and the scattering matrix completely characterize the given theory under asymptotic completeness and standard assumptions. Then we obtain several families of interacting wedge-local nets by a purely von Neumann algebraic procedure. One particular case of them coincides with the deformation of chiral CFT by Buchholz-Lechner-Summers. In another case, we manage to determine completely the strictly local elements. Finally, using Longo-Witten endomorphisms on the U(1)-current net and the free fermion net, a large family of wedge-local nets is constructed.
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