论文标题
缺少非交通性几何学的观点
Missing the point in noncommutative geometry
论文作者
论文摘要
非公共几何形状概括了标准平滑的几何形状，参数尺寸具有基本数量的尺寸的非交换性。然后出现问题，即在这种理论中，一个小于规模的区域的概念以及最终的概念是有意义的。我们认为它没有以两种相互关联的方式。在Connes的频谱三重方法的背景下，我们表明，任意小区域在形式意义上是无法定义的。在标量字段Moyal-Weyl方法中，我们表明他们不能给出操作定义。我们得出的结论是，这种几何形状不存在。因此，我们研究了（a）这种几何形状的形而上学，以及（b）如何将平滑歧管的出现恢复为基本非共同几何形状的近似值。
Noncommutative geometries generalize standard smooth geometries, parametrizing the noncommutativity of dimensions with a fundamental quantity with the dimensions of area. The question arises then of whether the concept of a region smaller than the scale - and ultimately the concept of a point - makes sense in such a theory. We argue that it does not, in two interrelated ways. In the context of Connes' spectral triple approach, we show that arbitrarily small regions are not definable in the formal sense. While in the scalar field Moyal-Weyl approach, we show that they cannot be given an operational definition. We conclude that points do not exist in such geometries. We therefore investigate (a) the metaphysics of such a geometry, and (b) how the appearance of smooth manifold might be recovered as an approximation to a fundamental noncommutative geometry.
