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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2508.13094 |
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| _version_ | 1866912747524980736 |
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| author | Maier, Robert S. |
| author_facet | Maier, Robert S. |
| contents | 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, but 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 a parametric exponential Riordan array of polynomial coefficients), called the Hsu-Shiue family. To yield orderings interpolating between normal and anti-normal, this family must be extended. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_13094 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sheffer Polynomials and the s-ordering of Exponential Boson Operators Maier, Robert S. Quantum Physics Mathematical Physics Combinatorics 81S30 (Primary) 81S05, 11B73 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, but 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 a parametric exponential Riordan array of polynomial coefficients), called the Hsu-Shiue family. To yield orderings interpolating between normal and anti-normal, this family must be extended. |
| title | Sheffer Polynomials and the s-ordering of Exponential Boson Operators |
| topic | Quantum Physics Mathematical Physics Combinatorics 81S30 (Primary) 81S05, 11B73 |
| url | https://arxiv.org/abs/2508.13094 |