有限量子模型：描述量子行为的构造性方法
Finite Quantum Models: Constructive Approach to Description of Quantum Behavior
摘要：
量子力学的普适性--它对性质和尺度完全不同的物理系统的适用性--表明量子行为可以是包含不可区分的系统的一般数学性质的表现，即位于某些对称群的相同轨道上的元素。在本文中，我们证明，量子行为自然出现在系统中的有限数量的元素连接的非平凡的对称群。“有限”的方法可以看到量子描述的特点更清楚，而不需要像“波函数崩溃”，“埃弗雷特的多重宇宙”等概念，特别是在有限性假设下，任何量子动力学减少到简单的置换动力学。有限量子模型的优点是可以通过计算机代数和计算群论方法来构造性地研究它们。
英文摘要：
Universality of quantum mechanics -- its applicability to physical systems of quite different nature and scales -- indicates that quantum behavior can be a manifestation of general mathematical properties of systems containing indistinguishable, i.e. lying on the same orbit of some symmetry group, elements. In this paper we demonstrate, that quantum behavior arises naturally in systems with finite number of elements connected by non-trivial symmetry groups. The "finite" approach allows to see the peculiarities of quantum description more distinctly without need for concepts like "wave function collapse", "Everett's multiverses" etc. In particular, under the finiteness assumption any quantum dynanics is reduced to the simple permutation dynamics. The advantage of the finite quantum models is that they can be studied constructively by means of computer algebra and computational group theory methods.
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