dorsal/arxiv
View SchemaBoson Normal Ordering via Substitutions and Sheffer-type Polynomials
| Authors | P Blasiak, A Horzela, K A Penson, G H E Duchamp, A I Solomon |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0501155 |
| URL | https://arxiv.org/abs/quant-ph/0501155 |
| DOI | 10.1016/j.physleta.2005.02.028 |
| Journal | Phys. Lett. A 338, 108 (2005) |
Abstract
We solve the boson normal ordering problem for (q(a*)a + v(a*))^n with arbitrary functions q and v and integer n, where a and a* are boson annihilation and creation operators, satisfying [a,a*]=1. This leads to exponential operators generalizing the shift operator and we show that their action can be expressed in terms of substitutions. Our solution is naturally related through the coherent state representation to the exponential generating functions of Sheffer-type polynomials. This in turn opens a vast arena of combinatorial methodology which is applied to boson normal ordering and illustrated by a few examples.
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"abstract": "We solve the boson normal ordering problem for (q(a*)a + v(a*))^n with\narbitrary functions q and v and integer n, where a and a* are boson\nannihilation and creation operators, satisfying [a,a*]=1. This leads to\nexponential operators generalizing the shift operator and we show that their\naction can be expressed in terms of substitutions. Our solution is naturally\nrelated through the coherent state representation to the exponential generating\nfunctions of Sheffer-type polynomials. This in turn opens a vast arena of\ncombinatorial methodology which is applied to boson normal ordering and\nillustrated by a few examples.",
"arxiv_id": "quant-ph/0501155",
"authors": [
"P Blasiak",
"A Horzela",
"K A Penson",
"G H E Duchamp",
"A I Solomon"
],
"categories": [
"quant-ph",
"math.CO"
],
"doi": "10.1016/j.physleta.2005.02.028",
"journal_ref": "Phys. Lett. A 338, 108 (2005)",
"title": "Boson Normal Ordering via Substitutions and Sheffer-type Polynomials",
"url": "https://arxiv.org/abs/quant-ph/0501155"
},
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