Monomiality principle, Sheffer-type polynomials and the normal ordering problem
英文摘要：
We solve the boson normal ordering problem for $(q(a^†)a+v(a^†))^n$ with arbitrary functions $q(x)$ and $v(x)$ and integer $n$, where $a$ and $a^†$ are boson annihilation and creation operators, satisfying $[a,a^†]=1$. This consequently provides the solution for the exponential $e^{λ(q(a^†)a+v(a^†))}$ generalizing the shift operator. In the course of these considerations we define and explore the monomiality principle and find its representations. We exploit the properties of Sheffer-type polynomials which constitute the inherent structure of this problem. In the end we give some examples illustrating the utility of the method and point out the relation to combinatorial structures.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
