有限量子系统的数学建模
Mathematical Modeling of Finite Quantum Systems
摘要：
我们考虑有限背景下的量子行为问题。在物理学中引入连续统或其他无限性只会导致技术上的复杂化，而在描述经验观测时不需要它们。有限的方法使问题的建设性和更容易处理。我们认为量子行为是动力系统对称性的自然结果。这是一个基本的不可能的跟踪身份的不可区分的对象在其演变的结果-只有信息不变的组合，这样的对象是可用的。我们证明，任何量子动力学可以嵌入到一个简单的置换动力学。量子现象，如干涉，出现在系统的对称群的置换表示的不变子空间中。可观测量可以用置换不变量来表示。
英文摘要：
We consider the problem of quantum behavior in the finite background. Introduction of continuum or other infinities into physics leads only to technical complications without any need for them in description of empirical observations. The finite approach makes the problem constructive and more tractable. We argue that quantum behavior is a natural consequence of symmetries of dynamical systems. It is a result of fundamental impossibility to trace identity of indistinguishable objects in their evolution - only information about invariant combinations of such objects is available. We demonstrate that any quantum dynamics can be embedded into a simple permutation dynamics. Quantum phenomena, such as interferences, arise in invariant subspaces of permutation representations of the symmetry group of a system. Observable quantities can be expressed in terms of the permutation invariants.
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