Algebraic Construction of the Basis for the Irreducible Representations of Rotation Groups and for the Homogeneous Lorentz Group
The basic functions for a class of the irreducible representations of the rotation groups in n dimensions (Rn ) are explicitly constructed by an algebraic method in which the basic functions are taken to be homogeneous polynomials in the variables of En . The solutions correspond to the hyperspheric...
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| Veröffentlicht in: | Journal of Mathematical Physics (New York) (U.S.) 1965-04, Vol.6 (4), p.578-583 |
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| container_end_page | 583 |
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| container_title | Journal of Mathematical Physics (New York) (U.S.) |
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| creator | Alcarás, J. A. Castilho Ferreira, P. Leal |
| description | The basic functions for a class of the irreducible representations of the rotation groups in n dimensions (Rn
) are explicitly constructed by an algebraic method in which the basic functions are taken to be homogeneous polynomials in the variables of En
. The solutions correspond to the hyperspherical harmonics of the mathematical literature and are of interest for problems exhibiting invariance under a certain Rn
. The method is also applied to derive a basis for the infinite‐dimensional irreducible representations of the homogeneous Lorentz group if we then look for homogeneous functions in the variables of the corresponding pseudo‐Euclidean space. |
| doi_str_mv | 10.1063/1.1704309 |
| format | Article |
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) are explicitly constructed by an algebraic method in which the basic functions are taken to be homogeneous polynomials in the variables of En
. The solutions correspond to the hyperspherical harmonics of the mathematical literature and are of interest for problems exhibiting invariance under a certain Rn
. The method is also applied to derive a basis for the infinite‐dimensional irreducible representations of the homogeneous Lorentz group if we then look for homogeneous functions in the variables of the corresponding pseudo‐Euclidean space.</description><identifier>ISSN: 0022-2488</identifier><identifier>EISSN: 1089-7658</identifier><identifier>DOI: 10.1063/1.1704309</identifier><identifier>CODEN: JMAPAQ</identifier><language>eng</language><subject>Elementary Particles and Radiations ; GROUP THEORY ; INVARIANCE PRINCIPLE ; IRREDUCIBLE REPRESENTATION ; LORENTZ TRANSFORMATIONS ; MATHEMATICS ; MATRICES ; PHYSICS ; POLYNOMIALS ; RELATIVITY THEORY ; ROTATION ; ROTATION GROUP ; SPHERICAL HARMONICS</subject><ispartof>Journal of Mathematical Physics (New York) (U.S.), 1965-04, Vol.6 (4), p.578-583</ispartof><rights>The American Institute of Physics</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c359t-e443871c069f75e17f5a2dc5ef69ff3bc77bb1f06585e34805fe02377352e23</citedby><cites>FETCH-LOGICAL-c359t-e443871c069f75e17f5a2dc5ef69ff3bc77bb1f06585e34805fe02377352e23</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://pubs.aip.org/jmp/article-lookup/doi/10.1063/1.1704309$$EHTML$$P50$$Gscitation$$H</linktohtml><link.rule.ids>314,780,784,885,1559,27924,27925,76390</link.rule.ids><backlink>$$Uhttps://www.osti.gov/biblio/4616405$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>Alcarás, J. A. Castilho</creatorcontrib><creatorcontrib>Ferreira, P. Leal</creatorcontrib><creatorcontrib>Instituto de Fisica Teorica, Sao Paulo, Brazil</creatorcontrib><title>Algebraic Construction of the Basis for the Irreducible Representations of Rotation Groups and for the Homogeneous Lorentz Group</title><title>Journal of Mathematical Physics (New York) (U.S.)</title><description>The basic functions for a class of the irreducible representations of the rotation groups in n dimensions (Rn
) are explicitly constructed by an algebraic method in which the basic functions are taken to be homogeneous polynomials in the variables of En
. The solutions correspond to the hyperspherical harmonics of the mathematical literature and are of interest for problems exhibiting invariance under a certain Rn
. The method is also applied to derive a basis for the infinite‐dimensional irreducible representations of the homogeneous Lorentz group if we then look for homogeneous functions in the variables of the corresponding pseudo‐Euclidean space.</description><subject>Elementary Particles and Radiations</subject><subject>GROUP THEORY</subject><subject>INVARIANCE PRINCIPLE</subject><subject>IRREDUCIBLE REPRESENTATION</subject><subject>LORENTZ TRANSFORMATIONS</subject><subject>MATHEMATICS</subject><subject>MATRICES</subject><subject>PHYSICS</subject><subject>POLYNOMIALS</subject><subject>RELATIVITY THEORY</subject><subject>ROTATION</subject><subject>ROTATION GROUP</subject><subject>SPHERICAL HARMONICS</subject><issn>0022-2488</issn><issn>1089-7658</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1965</creationdate><recordtype>article</recordtype><recordid>eNqdkMFLwzAYxYMoOKcH_4PgTaEzaZKmPc4xt8FAmN5Dm37ZKltTklTQk3-67Tr07unjffzeg_cQuqVkQknCHumESsIZyc7QiJI0i2Qi0nM0IiSOo5in6SW68v6dEEpTzkfoe7rfQuHySuOZrX1wrQ6VrbE1OOwAP-W-8thYd1Qr56BsdVXsAW-gceChDnnP-96wsYPAC2fbxuO8Ln-tS3uwW6jBth6vret8XwN2jS5Mvvdwc7pj9Po8f5sto_XLYjWbriPNRBYi4JylkmqSZEYKoNKIPC61ANM9DCu0lEVBDenaCmA8JcIAiZmUTMQQszG6G1KtD5Xyugqgd9rWNeigeEITTkQH3Q-QdtZ7B0Y1rjrk7lNRovp1FVWndTv2YWD7rGPr_8Ef1v2BqikN-wFRFIn4</recordid><startdate>196504</startdate><enddate>196504</enddate><creator>Alcarás, J. A. Castilho</creator><creator>Ferreira, P. Leal</creator><scope>AAYXX</scope><scope>CITATION</scope><scope>OTOTI</scope></search><sort><creationdate>196504</creationdate><title>Algebraic Construction of the Basis for the Irreducible Representations of Rotation Groups and for the Homogeneous Lorentz Group</title><author>Alcarás, J. A. Castilho ; Ferreira, P. Leal</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c359t-e443871c069f75e17f5a2dc5ef69ff3bc77bb1f06585e34805fe02377352e23</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1965</creationdate><topic>Elementary Particles and Radiations</topic><topic>GROUP THEORY</topic><topic>INVARIANCE PRINCIPLE</topic><topic>IRREDUCIBLE REPRESENTATION</topic><topic>LORENTZ TRANSFORMATIONS</topic><topic>MATHEMATICS</topic><topic>MATRICES</topic><topic>PHYSICS</topic><topic>POLYNOMIALS</topic><topic>RELATIVITY THEORY</topic><topic>ROTATION</topic><topic>ROTATION GROUP</topic><topic>SPHERICAL HARMONICS</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Alcarás, J. A. Castilho</creatorcontrib><creatorcontrib>Ferreira, P. Leal</creatorcontrib><creatorcontrib>Instituto de Fisica Teorica, Sao Paulo, Brazil</creatorcontrib><collection>CrossRef</collection><collection>OSTI.GOV</collection><jtitle>Journal of Mathematical Physics (New York) (U.S.)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Alcarás, J. A. Castilho</au><au>Ferreira, P. Leal</au><aucorp>Instituto de Fisica Teorica, Sao Paulo, Brazil</aucorp><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Algebraic Construction of the Basis for the Irreducible Representations of Rotation Groups and for the Homogeneous Lorentz Group</atitle><jtitle>Journal of Mathematical Physics (New York) (U.S.)</jtitle><date>1965-04</date><risdate>1965</risdate><volume>6</volume><issue>4</issue><spage>578</spage><epage>583</epage><pages>578-583</pages><issn>0022-2488</issn><eissn>1089-7658</eissn><coden>JMAPAQ</coden><abstract>The basic functions for a class of the irreducible representations of the rotation groups in n dimensions (Rn
) are explicitly constructed by an algebraic method in which the basic functions are taken to be homogeneous polynomials in the variables of En
. The solutions correspond to the hyperspherical harmonics of the mathematical literature and are of interest for problems exhibiting invariance under a certain Rn
. The method is also applied to derive a basis for the infinite‐dimensional irreducible representations of the homogeneous Lorentz group if we then look for homogeneous functions in the variables of the corresponding pseudo‐Euclidean space.</abstract><doi>10.1063/1.1704309</doi><tpages>6</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0022-2488 |
| ispartof | Journal of Mathematical Physics (New York) (U.S.), 1965-04, Vol.6 (4), p.578-583 |
| issn | 0022-2488 1089-7658 |
| language | eng |
| recordid | cdi_scitation_primary_10_1063_1_1704309 |
| source | AIP Digital Archive |
| subjects | Elementary Particles and Radiations GROUP THEORY INVARIANCE PRINCIPLE IRREDUCIBLE REPRESENTATION LORENTZ TRANSFORMATIONS MATHEMATICS MATRICES PHYSICS POLYNOMIALS RELATIVITY THEORY ROTATION ROTATION GROUP SPHERICAL HARMONICS |
| title | Algebraic Construction of the Basis for the Irreducible Representations of Rotation Groups and for the Homogeneous Lorentz Group |
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