1+1维无质量标量自由场，II：净上同调与超选择扇区的完备性
Massless scalar free Field in 1+1 dimensions, II: Net Cohomology and Completeness of Superselection Sectors
摘要：
作为Roberts上同调（净上同调）的一个应用，我们证明了标题中模型局部观测量的DHR扇区的完备性，详见[8]。这个结果是通过网1-上同调的平凡性实现的，其值在局部域中，将Roberts的方法增强到任意Weyl网的情况，不满足分裂性质。我们利用使用不同的因果指数集的网络所涉及的。引入由一般群分次的网的概念，以及分次局部性和分次对偶的相关性质，讨论了任意子对易关系的存在。作为进一步的结果，我们得到了该模型的扭曲扇区和非扭曲扇区作为W*-辫子范畴的两个对称子范畴的描述，其对象与规范对称性的紧阿贝尔群的对偶范畴相同.这一工作也为分析不同时空上一般模型的扇形结构提供了一些线索。
英文摘要：
As an application of Roberts' cohomology (net cohomology), we prove the completeness of the DHR sectors of the local observables of the model in the title, detailed in [8]. This result is achieved via the triviality of the net 1-cohomology, with values in the local fields, enhancing the Roberts' methods to the case of anyonic Weyl nets, not satisfying the split property. We take advantage of using different causal index sets for the nets involved. The presence of anyonic commutation relations is treated introducing the notion of nets graded by a generic group, and the related properties of graded locality and graded duality. As a further result, we obtain the description of twisted and untwisted sectors of the model as two symmetric subcategories of a W*-braided category, whose objects are the same as the dual category of the compact Abelian group of the gauge symmetry. The work also furnish some hints for the analysis of the sector structure of generic models on different spacetimes.
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