关于量子态的伪流形
On the pseudo-manifold of quantum states
摘要：
在物理学文献中有许多关于量子态分层的论述，例如关于酉群的轨道，以及关于酉群上的广义可微结构的论述，我们的目的是澄清和精确其中的一些论述。对于任意有限维C* 代数和A的酉元群U（A），我们观察到状态空间S（A）到U（A）轨道的划分不是分解，并且到轨道类型的分解不是分层（它的片不是无边界流形），而存在到固定秩矩阵的自然Whitney分层。对于后者，当A是满矩阵代数时，我们给出了伪流形结构（任意点周围的圆锥邻域）的明确描述。然后，我们对无限维的情况做了一些评论。
英文摘要：
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.
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