Sheffer Polynomials and the s-ordering of Exponential Boson Operators
- URL: http://arxiv.org/abs/2508.13094v1
- Date: Mon, 18 Aug 2025 17:05:40 GMT
- Title: Sheffer Polynomials and the s-ordering of Exponential Boson Operators
- Authors: Robert S. Maier,
- Abstract summary: S-ordering concept originated in quantum optics, and subsumes normal, symmetric, and anti-normal ordering.<n>S-ordered expressions are derived with the aid of a parametric family of Sheffer sequences.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The s-ordered form of any product of single-mode boson creation and annihilation operators, containing only a single annihilator, is computed explicitly. The s-ordering concept originated in quantum optics, and subsumes normal, symmetric (Weyl), and anti-normal ordering for any two operators satisfying a canonical commutation relation. Because the s-ordering map can be viewed as producing a function of a complex variable, its inverse is a quantization map that takes such "classical" functions to quantum operators. The explicit s-ordered expressions are derived with the aid of a parametric family of Sheffer polynomial sequences (or equivalently an exponential Riordan array of polynomial coefficients), called the Hsu-Shiue family. To yield orderings interpolating between normal and anti-normal, this family is extended in an intricate way.
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