论文标题
在量子状态的伪模型上
On the pseudo-manifold of quantum states
论文作者
论文摘要
物理学文献中有各种陈述有关量子状态分层的陈述，例如统一组的轨道以及其上的通用可区分结构。我们的目的是澄清并精确一些这些陈述。对于一个任意的有限维c*algebra和u（a）a的单一元素组，我们观察到，状态空间s（a）中s（a）在u（a）轨道中的划分不是分解，并且分解为轨道类型不是分层的（没有分层的零件是没有边界的），同时固定了自然成熟的构图。对于后者，当a是完整的矩阵代数时，我们将对伪模型结构（任何点附近的圆锥形邻域）进行明确的描述。然后，我们对无限维情况发表了一些评论。
There are various statements in the physics literature about the stratification of quantum states, for example into orbits of a unitary group, and about generalized differentiable structures on it. Our aim is to clarify and make precise some of these statements. For A an arbitrary finite-dimensional C*-algebra and U(A) the group of unitary elements of A, we observe that the partition of the state space S(A) into U(A) orbits is not a decomposition and that the decomposition into orbit types is not a stratification (its pieces are not manifolds without boundary), while there is a natural Whitney stratification into matrices of fixed rank. For the latter, when A is a full matrix algebra, we give an explicit description of the pseudo-manifold structure (the conical neighborhood around any point). We then make some comments about the infinite-dimensional case.
