dorsal/arxiv
View SchemaCombinatorics of boson normal ordering and some applications
| Authors | P. Blasiak |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0507206 |
| URL | https://arxiv.org/abs/quant-ph/0507206 |
| Journal | Concepts of Physics 1, 177-278 (2004) |
Abstract
We provide the solution to the normal ordering problem for powers and exponentials of two classes of operators. The first one consists of boson strings and more generally homogeneous polynomials, while the second one treats operators linear in one of the creation or annihilation operators. Both solutions generalize Bell and Stirling numbers arising in the number operator case. We use the advanced combinatorial analysis to provide closed form expressions, generating functions, recurrences, etc. The analysis is based on the Dobi\'nski-type relations and the umbral calculus methods. As an illustration of this framework we point out the applications to the construction of generalized coherent states, operator calculus and ordering of deformed bosons.
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"abstract": "We provide the solution to the normal ordering problem for powers and\nexponentials of two classes of operators. The first one consists of boson\nstrings and more generally homogeneous polynomials, while the second one treats\noperators linear in one of the creation or annihilation operators. Both\nsolutions generalize Bell and Stirling numbers arising in the number operator\ncase. We use the advanced combinatorial analysis to provide closed form\nexpressions, generating functions, recurrences, etc. The analysis is based on\nthe Dobi\\\u0027nski-type relations and the umbral calculus methods. As an\nillustration of this framework we point out the applications to the\nconstruction of generalized coherent states, operator calculus and ordering of\ndeformed bosons.",
"arxiv_id": "quant-ph/0507206",
"authors": [
"P. Blasiak"
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"journal_ref": "Concepts of Physics 1, 177-278 (2004)",
"title": "Combinatorics of boson normal ordering and some applications",
"url": "https://arxiv.org/abs/quant-ph/0507206"
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