论文标题
海森堡换向关系的有限扰动通过扩张理论
Bounded perturbations of the Heisenberg commutation relation via dilation theory
论文作者
论文摘要
我们将扩张距离的概念扩展到强烈连续的单参数单一群体。如果两个这样的组之间的扩张距离是有限的，那么这些组可以在同一空间上表示其发电机具有相同域并且实际上是彼此界定的扰动。该结果扩展到单参数统一组的D-tupers。我们将结果应用于Weyl典型的换向关系，作为一种特殊情况，我们恢复了Haagerup和Rordam的结果，即规范位置和动量运算符的无限放大使Heisenberg换向关系的无限放大是一对强有力的自动化自动关联运营商的界限。我们还恢复了GAO对Haagerup和Rordam结果的高维概括，在典型情况下，我们会显着改善尺寸增长时对界限的控制。
We extend the notion of dilation distance to strongly continuous one-parameter unitary groups. If the dilation distance between two such groups is finite, then these groups can be represented on the same space in such a way that their generators have the same domain and are in fact a bounded perturbation of one another. This result extends to d-tuples of one-parameter unitary groups. We apply our results to the Weyl canonical commutation relations, and as a special case we recover the result of Haagerup and Rordam that the infinite ampliation of the canonical position and momentum operators satisfying the Heisenberg commutation relation are a bounded perturbation of a pair of strongly commuting selfadjoint operators. We also recover Gao's higher-dimensional generalization of Haagerup and Rordam's result, and in typical cases we significantly improve control of the bound when the dimension grows.
