组合物理中的阶梯算子与自同态
Ladder Operators and Endomorphisms in Combinatorial Physics
摘要：
从海森堡-外尔代数开始，量子物理学的基础，我们首先展示了该代数内在的非对易算子的排序如何产生组合学经典斯特林数的推广。这些可以用无限但{ \em行有限}的矩阵来表示，这些矩阵也可以被认为是$\C[[x]]$的自同态。这使我们考虑更一般空间中的自同态，而这些又可以用物理学中熟悉的梯形算子的推广来表示。
英文摘要：
Starting with the Heisenberg-Weyl algebra, fundamental to quantum physics, we first show how the ordering of the non-commuting operators intrinsic to that algebra gives rise to generalizations of the classical Stirling Numbers of Combinatorics. These may be expressed in terms of infinite, but {\em row-finite}, matrices, which may also be considered as endomorphisms of $\C[[x]]$. This leads us to consider endomorphisms in more general spaces, and these in turn may be expressed in terms of generalizations of the ladder-operators familiar in physics.
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