格点上的影演算、离散化和量子力学
Umbral Calculus, Discretization, and Quantum Mechanics on a Lattice
摘要：
“Umbral calculus”处理正则对易关系的表示。我们提出了一个简短的论述，并讨论如何使用这种演算离散连续模型和构造表示的李代数格。相关的想法出现在最近的出版物，我们表明，有特殊情况下的阴影演算的例子。这一观察结果表明，这些例子的各种概括。本文详细研究了格点上正则对易关系的位置和动量算符的一种特殊的影表示。
英文摘要：
`Umbral calculus' deals with representations of the canonical commutation relations. We present a short exposition of it and discuss how this calculus can be used to discretize continuum models and to construct representations of Lie algebras on a lattice. Related ideas appeared in recent publications and we show that the examples treated there are special cases of umbral calculus. This observation then suggests various generalizations of these examples. A special umbral representation of the canonical commutation relations given in terms of the position and momentum operator on a lattice is investigated in detail.
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