Moebius协变理论中的局部化算子和位置算子
On localization and position operators in Moebius-covariant theories
摘要：
几年前，有人指出，在某些情况下，定域性的概念可以从理论所享有的对称群中产生，因此是以内在的方式产生的。特别地，当存在Moebius协方差时，可以将一些特定的变换与Tomita Takesaki模算子和抽象圆的特定区间的共轭相关联。在这种情况下，我们提出了一种定义表示与模变换共轭的坐标的运算符的方法。值得注意的是，这个坐标与抽象的定域性概念是相容的。最后给出了一个关于直线上量子粒子的具体例子。
英文摘要：
Some years ago it was shown that, in some cases, a notion of locality can arise from the group of symmetry enjoyed by the theory, thus in an intrinsic way. In particular, when Moebius covariance is present, it is possible to associate some particular transformations to the Tomita Takesaki modular operator and conjugation of a specific interval of an abstract circle. In this context we propose a way to define an operator representing the coordinate conjugated with the modular transformations. Remarkably this coordinate turns out to be compatible with the abstract notion of locality. Finally a concrete example concerning a quantum particle on a line is also given.
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