量子点/模式，第1部分。从几何点到量子点
Quantum points/patterns, Part 1. From geometrical points to quantum points in a sheaf framework
摘要：
我们考虑量子态理论的一些推广，这是基于长期存在的问题和不令人满意的情况与量子力学的可能解释的分析。我们证明，考虑量子态作为层，可以提供，在原则上，更深入的理解一些现象。建议的建设的关键成分是家庭的部分层的值在类别的功能实现的无限维希尔伯特空间与特殊（多尺度）过滤。三种不同的对称性，运动学的（在时空上），隐藏/动力学的（在层的截面上），统一的（在空间的全尺度的过滤上）是产生量子现象的完整动物园的通用对象（例如，比光传播更快）。
英文摘要：
We consider some generalization of the theory of quantum states, which is based on the analysis of long standing problems and unsatisfactory situation with the possible interpretations of quantum mechanics. We demonstrate that the consideration of quantum states as sheaves can provide, in principle, more deep understanding of some phenomena. The key ingredients of the proposed construction are the families of sections of sheaves with values in the category of the functional realizations of infinite-dimensional Hilbert spaces with special (multiscale) filtration. Three different symmetries, kinematical (on space-time), hidden/dynamical (on sections of sheaves), unified (on filtration of the full scale of spaces) are generic objects generating the full zoo of quantum phenomena (e.g., faster than light propagation).
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