典型交换关系的C* 代数-代数的完全正则性。（已添加勘误）
Full regularity for a C*-algebra of the Canonical Commutation Relations. (Erratum added)
摘要：
Weyl代数--通常用来模拟正则对易关系（CCR）的C* 代数，有一个众所周知的缺陷，即它有大量不规则的表示，这些表示不能模拟物理场。本文明确构造了一个C* 代数，它能再现可数维辛空间（S，B）的CCR，并且它的表示集恰好是CCR的正则表示的全集.这种构造使用Blackadar版本的非单位C* 代数的无限张量积，并且它产生了阿贝尔群S的σ-表示论的“宿主代数”（即广义群代数，下面解释），其中σ（.，.）：e^{iB（.，.）/ 2}。作为一个简单的应用，它随后得出，对于可分希尔伯特空间上的（S，B）的Weyl代数的每一个正则表示，都有一个直接的积分分解为不可约的正则表示（一个已知的结果）。本文最后补充了一个勘误。
英文摘要：
The Weyl algebra,- the usual C*-algebra employed to model the canonical commutation relations (CCRs), has a well-known defect in that it has a large number of representations which are not regular and these cannot model physical fields. Here, we construct explicitly a C*-algebra which can reproduce the CCRs of a countably dimensional symplectic space (S,B) and such that its representation set is exactly the full set of regular representations of the CCRs. This construction uses Blackadar's version of infinite tensor products of nonunital C*-algebras, and it produces a "host algebra" (i.e. a generalised group algebra, explained below) for the σ-representation theory of the abelian group S where σ(.,.):=e^{iB(.,.)/2}. As an easy application, it then follows that for every regular representation of the Weyl algebra of (S,B) on a separable Hilbert space, there is a direct integral decomposition of it into irreducible regular representations (a known result). An Erratum for this paper is added at the end.
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