dorsal/arxiv
View SchemaCombinatorics of Boson Normal Ordering: the Dobinski Formula Revisited
| Authors | Karol A. Penson, Allan I. Solomon |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0211028 |
| URL | https://arxiv.org/abs/quant-ph/0211028 |
Abstract
We derive explicit formulas for the normal ordering of powers of arbitrary monomials of boson operators. These formulas lead to generalisations of conventional Bell and Stirling numbers and to appropriate generalisations of the Dobinski relations. These new combinatorial numbers are shown to be coherent state matrix elements of powers of the monomials in question. It is further demonstrated that such Bell-type numbers, when considered as power moments, give rise to positive measures on the positive half-axis, which in many cases can be written in terms of known functions.
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"abstract": "We derive explicit formulas for the normal ordering of powers of arbitrary\nmonomials of boson operators. These formulas lead to generalisations of\nconventional Bell and Stirling numbers and to appropriate generalisations of\nthe Dobinski relations. These new combinatorial numbers are shown to be\ncoherent state matrix elements of powers of the monomials in question. It is\nfurther demonstrated that such Bell-type numbers, when considered as power\nmoments, give rise to positive measures on the positive half-axis, which in\nmany cases can be written in terms of known functions.",
"arxiv_id": "quant-ph/0211028",
"authors": [
"Karol A. Penson",
"Allan I. Solomon"
],
"categories": [
"quant-ph",
"math.CO"
],
"title": "Combinatorics of Boson Normal Ordering: the Dobinski Formula Revisited",
"url": "https://arxiv.org/abs/quant-ph/0211028"
},
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"variant": "snapshot-2026-03-01",
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