论文标题
dirac和weyl-von neumann代数的正常状态
Dirac and normal states on Weyl-von Neumann algebras
论文作者
论文摘要
我们研究了与符号矢量空间$ s $相关的Weyl代数$ \ Mathcal {W} $以及以$ \ Mathcal {W} $表示的von Neumann代数相关的特定类别。量子物理中的应用需要实现约束方程，例如，由于量规条件，可以基于所谓的狄拉克状态。状态可以以$ s $上的非线性函数为特征，事实证明，那些与非平凡的狄拉克状态相对应的人通常是不连续的。我们讨论了$ s $和各州函数之间这种相互作用的一般方面，但也为非平凡的迪拉克状态的特定示例类别进行了分析。在最后一部分中，我们专注于$ s = l^2（\ mathbb {r}^n）$或在$ \ mathbb {r}^n $上的测试功能，并将国家属性与$ \ mathcal {w} $上的属性与$ \ mathbb {r}^n $的广义功能上的属性和有害分析的广义功能相关联。温带分布。
We study particular classes of states on the Weyl algebra $\mathcal{W}$ associated with a symplectic vector space $S$ and on the von Neumann algebras generated in representations of $\mathcal{W}$. Applications in quantum physics require an implementation of constraint equations, e.g., due to gauge conditions, and can be based on so-called Dirac states. The states can be characterized by nonlinear functions on $S$ and it turns out that those corresponding to non-trivial Dirac states are typically discontinuous. We discuss general aspects of this interplay between functions on $S$ and states, but also develop an analysis for a particular example class of non-trivial Dirac states. In the last part, we focus on the specific situation with $S = L^2(\mathbb{R}^n)$ or test functions on $\mathbb{R}^n$ and relate properties of states on $\mathcal{W}$ with those of generalized functions on $\mathbb{R}^n$ or with harmonic analysis aspects of corresponding Borel measures on Schwartz functions and on temperate distributions.
