Monomiality principle, Sheffer-type polynomials and the normal ordering problem

We solve the boson normal ordering problem for (q(a†)a + v(a†))n with arbitrary functions q(x) and v(x) and integer n, where a and a† are boson annihilation and creation operators, satisfying [a, a†] 1. This consequently provides the solution for the exponential eλ(q(a†)a + v(a†)) generalizing the s...

Full description

Saved in:
Bibliographic Details
Published in:Journal of physics. Conference series 2006-02, Vol.30 (1), p.86-97
Main Authors: Penson, K A, Blasiak, P, Dattoli, G, Duchamp, G H E, Horzela, A, Solomon, A I
Format: Article
Language:English
Subjects:
Combinatorial analysis
Mathematical analysis
Physics
Polynomials
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c391t-909ac8ab5ce9c379f3ca4d1d0f113f63325edff81794147f0a5bf3d6823b27423
cites cdi_FETCH-LOGICAL-c391t-909ac8ab5ce9c379f3ca4d1d0f113f63325edff81794147f0a5bf3d6823b27423
container_end_page 97
container_issue 1
container_start_page 86
container_title Journal of physics. Conference series
container_volume 30
creator Penson, K A
Blasiak, P
Dattoli, G
Duchamp, G H E
Horzela, A
Solomon, A I
description We solve the boson normal ordering problem for (q(a†)a + v(a†))n with arbitrary functions q(x) and v(x) and integer n, where a and a† are boson annihilation and creation operators, satisfying [a, a†] 1. This consequently provides the solution for the exponential eλ(q(a†)a + v(a†)) generalizing the shift operator. In the course of these considerations we define and explore the monomiality principle and find its representations. We exploit the properties of Sheffer-type polynomials which constitute the inherent structure of this problem. In the end we give some examples illustrating the utility of the method and point out the relation to combinatorial structures.
doi_str_mv 10.1088/1742-6596/30/1/012
format article
fullrecord <record><control><sourceid>proquest_iop_p</sourceid><recordid>TN_cdi_proquest_journals_2580729927</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2580729927</sourcerecordid><originalsourceid>FETCH-LOGICAL-c391t-909ac8ab5ce9c379f3ca4d1d0f113f63325edff81794147f0a5bf3d6823b27423</originalsourceid><addsrcrecordid>eNqNkE1LxDAQhoMouK7-AU8BT4K1SaZtmqMsfoGyB_Uc0ny4Xdqmpt1D_71ZKiLowbnMMDzvvMyL0Dkl15SUZUp5xpIiF0UKJKUpoewALb6Xhz_mY3QyDFtCIBZfoPWz73xbq6YeJ9yHutN139gr_LKxztmQjFNvce-baaYGrDqDx43FnQ-tarAPxkbVe9T6qrHtKTpyEbNnX32J3u5uX1cPydP6_nF185RoEHRMBBFKl6rKtRUauHCgVWaoIY5ScAUAy61xrqRcZDTjjqi8cmCKkkHF4iuwRBfz3ej7sbPDKLd-F7poKVleEs6EYDxSbKZ08MMQrJPxxVaFSVIi98HJfS5yn4uEuJExuChKZlHt-__xl3_wvzjZGwefbJR7Uw</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2580729927</pqid></control><display><type>article</type><title>Monomiality principle, Sheffer-type polynomials and the normal ordering problem</title><source>Publicly Available Content Database</source><source>Free Full-Text Journals in Chemistry</source><creator>Penson, K A ; Blasiak, P ; Dattoli, G ; Duchamp, G H E ; Horzela, A ; Solomon, A I</creator><creatorcontrib>Penson, K A ; Blasiak, P ; Dattoli, G ; Duchamp, G H E ; Horzela, A ; Solomon, A I</creatorcontrib><description>We solve the boson normal ordering problem for (q(a†)a + v(a†))n with arbitrary functions q(x) and v(x) and integer n, where a and a† are boson annihilation and creation operators, satisfying [a, a†] 1. This consequently provides the solution for the exponential eλ(q(a†)a + v(a†)) generalizing the shift operator. In the course of these considerations we define and explore the monomiality principle and find its representations. We exploit the properties of Sheffer-type polynomials which constitute the inherent structure of this problem. In the end we give some examples illustrating the utility of the method and point out the relation to combinatorial structures.</description><identifier>ISSN: 1742-6596</identifier><identifier>ISSN: 1742-6588</identifier><identifier>EISSN: 1742-6596</identifier><identifier>DOI: 10.1088/1742-6596/30/1/012</identifier><language>eng</language><publisher>Bristol: IOP Publishing</publisher><subject>Combinatorial analysis ; Mathematical analysis ; Physics ; Polynomials</subject><ispartof>Journal of physics. Conference series, 2006-02, Vol.30 (1), p.86-97</ispartof><rights>Copyright IOP Publishing Feb 2006</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c391t-909ac8ab5ce9c379f3ca4d1d0f113f63325edff81794147f0a5bf3d6823b27423</citedby><cites>FETCH-LOGICAL-c391t-909ac8ab5ce9c379f3ca4d1d0f113f63325edff81794147f0a5bf3d6823b27423</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.proquest.com/docview/2580729927?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,25753,27924,27925,37012,44590</link.rule.ids></links><search><creatorcontrib>Penson, K A</creatorcontrib><creatorcontrib>Blasiak, P</creatorcontrib><creatorcontrib>Dattoli, G</creatorcontrib><creatorcontrib>Duchamp, G H E</creatorcontrib><creatorcontrib>Horzela, A</creatorcontrib><creatorcontrib>Solomon, A I</creatorcontrib><title>Monomiality principle, Sheffer-type polynomials and the normal ordering problem</title><title>Journal of physics. Conference series</title><description>We solve the boson normal ordering problem for (q(a†)a + v(a†))n with arbitrary functions q(x) and v(x) and integer n, where a and a† are boson annihilation and creation operators, satisfying [a, a†] 1. This consequently provides the solution for the exponential eλ(q(a†)a + v(a†)) generalizing the shift operator. In the course of these considerations we define and explore the monomiality principle and find its representations. We exploit the properties of Sheffer-type polynomials which constitute the inherent structure of this problem. In the end we give some examples illustrating the utility of the method and point out the relation to combinatorial structures.</description><subject>Combinatorial analysis</subject><subject>Mathematical analysis</subject><subject>Physics</subject><subject>Polynomials</subject><issn>1742-6596</issn><issn>1742-6588</issn><issn>1742-6596</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2006</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><recordid>eNqNkE1LxDAQhoMouK7-AU8BT4K1SaZtmqMsfoGyB_Uc0ny4Xdqmpt1D_71ZKiLowbnMMDzvvMyL0Dkl15SUZUp5xpIiF0UKJKUpoewALb6Xhz_mY3QyDFtCIBZfoPWz73xbq6YeJ9yHutN139gr_LKxztmQjFNvce-baaYGrDqDx43FnQ-tarAPxkbVe9T6qrHtKTpyEbNnX32J3u5uX1cPydP6_nF185RoEHRMBBFKl6rKtRUauHCgVWaoIY5ScAUAy61xrqRcZDTjjqi8cmCKkkHF4iuwRBfz3ej7sbPDKLd-F7poKVleEs6EYDxSbKZ08MMQrJPxxVaFSVIi98HJfS5yn4uEuJExuChKZlHt-__xl3_wvzjZGwefbJR7Uw</recordid><startdate>20060228</startdate><enddate>20060228</enddate><creator>Penson, K A</creator><creator>Blasiak, P</creator><creator>Dattoli, G</creator><creator>Duchamp, G H E</creator><creator>Horzela, A</creator><creator>Solomon, A I</creator><general>IOP Publishing</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>H8D</scope><scope>HCIFZ</scope><scope>L7M</scope><scope>P5Z</scope><scope>P62</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope></search><sort><creationdate>20060228</creationdate><title>Monomiality principle, Sheffer-type polynomials and the normal ordering problem</title><author>Penson, K A ; Blasiak, P ; Dattoli, G ; Duchamp, G H E ; Horzela, A ; Solomon, A I</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c391t-909ac8ab5ce9c379f3ca4d1d0f113f63325edff81794147f0a5bf3d6823b27423</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2006</creationdate><topic>Combinatorial analysis</topic><topic>Mathematical analysis</topic><topic>Physics</topic><topic>Polynomials</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Penson, K A</creatorcontrib><creatorcontrib>Blasiak, P</creatorcontrib><creatorcontrib>Dattoli, G</creatorcontrib><creatorcontrib>Duchamp, G H E</creatorcontrib><creatorcontrib>Horzela, A</creatorcontrib><creatorcontrib>Solomon, A I</creatorcontrib><collection>CrossRef</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>Advanced Technologies &amp; Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>AUTh Library subscriptions: ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>Aerospace Database</collection><collection>SciTech Premium Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>ProQuest advanced technologies &amp; aerospace journals</collection><collection>ProQuest Advanced Technologies &amp; Aerospace Collection</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><jtitle>Journal of physics. Conference series</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Penson, K A</au><au>Blasiak, P</au><au>Dattoli, G</au><au>Duchamp, G H E</au><au>Horzela, A</au><au>Solomon, A I</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Monomiality principle, Sheffer-type polynomials and the normal ordering problem</atitle><jtitle>Journal of physics. Conference series</jtitle><date>2006-02-28</date><risdate>2006</risdate><volume>30</volume><issue>1</issue><spage>86</spage><epage>97</epage><pages>86-97</pages><issn>1742-6596</issn><issn>1742-6588</issn><eissn>1742-6596</eissn><abstract>We solve the boson normal ordering problem for (q(a†)a + v(a†))n with arbitrary functions q(x) and v(x) and integer n, where a and a† are boson annihilation and creation operators, satisfying [a, a†] 1. This consequently provides the solution for the exponential eλ(q(a†)a + v(a†)) generalizing the shift operator. In the course of these considerations we define and explore the monomiality principle and find its representations. We exploit the properties of Sheffer-type polynomials which constitute the inherent structure of this problem. In the end we give some examples illustrating the utility of the method and point out the relation to combinatorial structures.</abstract><cop>Bristol</cop><pub>IOP Publishing</pub><doi>10.1088/1742-6596/30/1/012</doi><tpages>12</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 1742-6596
ispartof Journal of physics. Conference series, 2006-02, Vol.30 (1), p.86-97
issn 1742-6596
1742-6588
1742-6596
language eng
recordid cdi_proquest_journals_2580729927
source Publicly Available Content Database; Free Full-Text Journals in Chemistry
subjects Combinatorial analysis
Mathematical analysis
Physics
Polynomials
title Monomiality principle, Sheffer-type polynomials and the normal ordering problem
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-26T06%3A45%3A54IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_iop_p&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Monomiality%20principle,%20Sheffer-type%20polynomials%20and%20the%20normal%20ordering%20problem&rft.jtitle=Journal%20of%20physics.%20Conference%20series&rft.au=Penson,%20K%20A&rft.date=2006-02-28&rft.volume=30&rft.issue=1&rft.spage=86&rft.epage=97&rft.pages=86-97&rft.issn=1742-6596&rft.eissn=1742-6596&rft_id=info:doi/10.1088/1742-6596/30/1/012&rft_dat=%3Cproquest_iop_p%3E2580729927%3C/proquest_iop_p%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c391t-909ac8ab5ce9c379f3ca4d1d0f113f63325edff81794147f0a5bf3d6823b27423%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=2580729927&rft_id=info:pmid/&rfr_iscdi=true