玻色正规序的代换和Sheffer型多项式
Boson Normal Ordering via Substitutions and Sheffer-type Polynomials
摘要：
我们解决了（q（a*）a + v（a*））^n的玻色子正规序问题，其中任意函数q和v以及整数n，其中a和a* 是玻色子湮灭和产生算子，满足[a，a*]=1。这导致指数算子推广的移位算子，我们表明，他们的行动可以表示在替代方面。我们的解决方案是自然相关的，通过相干态表示的指数生成函数的谢弗型多项式。这反过来又打开了一个广阔的舞台组合方法，适用于玻色子正常秩序和说明了几个例子。
英文摘要：
We solve the boson normal ordering problem for (q(a*)a + v(a*))^n with arbitrary functions q and v and integer n, where a and a* are boson annihilation and creation operators, satisfying [a,a*]=1. This leads to exponential operators generalizing the shift operator and we show that their action can be expressed in terms of substitutions. Our solution is naturally related through the coherent state representation to the exponential generating functions of Sheffer-type polynomials. This in turn opens a vast arena of combinatorial methodology which is applied to boson normal ordering and illustrated by a few examples.
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