dorsal/arxiv
View SchemaThe general boson normal ordering problem
| Authors | Pawel Blasiak, Karol A. Penson, Allan I. Solomon |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0402027 |
| URL | https://arxiv.org/abs/quant-ph/0402027 |
| DOI | 10.1016/S0375-9601(03)00194-4 |
| Journal | Physics Letters A, 309, 198 (2003) |
Abstract
We solve the boson normal ordering problem for F[(a*)^r a^s], with r,s positive integers, where a* and a are boson creation and annihilation operators satisfying [a,a*]=1. That is, we provide exact and explicit expressions for the normal form wherein all a's are to the right. The solution involves integer sequences of numbers which are generalizations of the conventional Bell and Stirling numbers whose values they assume for r=s=1. A comprehensive theory of such generalized combinatorial numbers is given including closed-form expressions (extended Dobinski-type formulas)and generating functions. These last are special expectation values in boson coherent states.
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"abstract": "We solve the boson normal ordering problem for F[(a*)^r a^s], with r,s\npositive integers, where a* and a are boson creation and annihilation operators\nsatisfying [a,a*]=1. That is, we provide exact and explicit expressions for the\nnormal form wherein all a\u0027s are to the right. The solution involves integer\nsequences of numbers which are generalizations of the conventional Bell and\nStirling numbers whose values they assume for r=s=1. A comprehensive theory of\nsuch generalized combinatorial numbers is given including closed-form\nexpressions (extended Dobinski-type formulas)and generating functions. These\nlast are special expectation values in boson coherent states.",
"arxiv_id": "quant-ph/0402027",
"authors": [
"Pawel Blasiak",
"Karol A. Penson",
"Allan I. Solomon"
],
"categories": [
"quant-ph",
"math.CO"
],
"doi": "10.1016/S0375-9601(03)00194-4",
"journal_ref": "Physics Letters A, 309, 198 (2003)",
"title": "The general boson normal ordering problem",
"url": "https://arxiv.org/abs/quant-ph/0402027"
},
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