dorsal/arxiv
View SchemaRepresentations of Monomiality Principle with Sheffer-type Polynomials and Boson Normal Ordering
| Authors | P Blasiak, G Dattoli, A Horzela, K A Penson |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0504009 |
| URL | https://arxiv.org/abs/quant-ph/0504009 |
| DOI | 10.1016/j.physleta.2005.11.052 |
| Journal | Phys. Lett. A 352, 7-12 (2006) |
Abstract
We construct explicit representations of the Heisenberg-Weyl algebra [P,M]=1 in terms of ladder operators acting in the space of Sheffer-type polynomials. Thus we establish a link between the monomiality principle and the umbral calculus. We use certain operator identities which allow one to evaluate explicitly special boson matrix elements between the coherent states. This yields a general demonstration of boson normal ordering of operator functions linear in either creation or annihilation operators. We indicate possible applications of these methods in other fields.
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"abstract": "We construct explicit representations of the Heisenberg-Weyl algebra [P,M]=1\nin terms of ladder operators acting in the space of Sheffer-type polynomials.\nThus we establish a link between the monomiality principle and the umbral\ncalculus. We use certain operator identities which allow one to evaluate\nexplicitly special boson matrix elements between the coherent states. This\nyields a general demonstration of boson normal ordering of operator functions\nlinear in either creation or annihilation operators. We indicate possible\napplications of these methods in other fields.",
"arxiv_id": "quant-ph/0504009",
"authors": [
"P Blasiak",
"G Dattoli",
"A Horzela",
"K A Penson"
],
"categories": [
"quant-ph"
],
"doi": "10.1016/j.physleta.2005.11.052",
"journal_ref": "Phys. Lett. A 352, 7-12 (2006)",
"title": "Representations of Monomiality Principle with Sheffer-type Polynomials and Boson Normal Ordering",
"url": "https://arxiv.org/abs/quant-ph/0504009"
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