关于Urn模型、非交换性和算子范式
On Urn Models, Non-commutativity and Operator Normal Forms
摘要：
非交换性在现实的数学建模中无处不在，在许多情况下，相同的代数结构在不同的情况下实现。本文考虑量子理论的正则对易关系，并讨论后者的一个简单的瓮模型。它表明，计数瓮历史提供了一个忠实的实现海森堡-外尔代数。利用这个类比，我们演示了如何运营商的正规形式促进计数的历史，通过生成函数，这反过来又产生一个直观的组合图片的排序过程本身。
英文摘要：
Non-commutativity is ubiquitous in mathematical modeling of reality and in many cases same algebraic structures are implemented in different situations. Here we consider the canonical commutation relation of quantum theory and discuss a simple urn model of the latter. It is shown that enumeration of urn histories provides a faithful realization of the Heisenberg-Weyl algebra. Drawing on this analogy we demonstrate how the operator normal forms facilitate counting of histories via generating functions, which in turn yields an intuitive combinatorial picture of the ordering procedure itself.
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