Racah Coefficients for the Group SL(2,ℝ)
The paper is devoted to the derivation of a universal integral representation for 6 j -symbols, or Racah coefficients, for the tensor product of three unitary representations of the principle series of the group SL(2, ℝ). The problem of calculating 6 j -symbols admits a natural reformulation in the...
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| Veröffentlicht in: | Journal of mathematical sciences (New York, N.Y.) N.Y.), 2023-09, Vol.275 (3), p.289-298 |
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| container_title | Journal of mathematical sciences (New York, N.Y.) |
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| creator | Derkachev, S. E. Ivanov, A. V. |
| description | The paper is devoted to the derivation of a universal integral representation for 6
j
-symbols, or Racah coefficients, for the tensor product of three unitary representations of the principle series of the group SL(2, ℝ). The problem of calculating 6
j
-symbols admits a natural reformulation in the language of Feynman diagrams. The original diagram can be significantly simplified and reduced to a basic diagram using the Gorishnii–Isaev method. In the case of representations of the principle series, we obtained a closed expression in the form of the Mellin–Barnes integral for the basic diagram. |
| doi_str_mv | 10.1007/s10958-023-06681-x |
| format | Article |
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j
-symbols, or Racah coefficients, for the tensor product of three unitary representations of the principle series of the group SL(2, ℝ). The problem of calculating 6
j
-symbols admits a natural reformulation in the language of Feynman diagrams. The original diagram can be significantly simplified and reduced to a basic diagram using the Gorishnii–Isaev method. In the case of representations of the principle series, we obtained a closed expression in the form of the Mellin–Barnes integral for the basic diagram.</description><identifier>ISSN: 1072-3374</identifier><identifier>EISSN: 1573-8795</identifier><identifier>DOI: 10.1007/s10958-023-06681-x</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Feynman diagrams ; Mathematical analysis ; Mathematics ; Mathematics and Statistics ; Principles ; Representations ; Symbols ; Tensors</subject><ispartof>Journal of mathematical sciences (New York, N.Y.), 2023-09, Vol.275 (3), p.289-298</ispartof><rights>Springer Nature Switzerland AG 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><rights>COPYRIGHT 2023 Springer</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c368x-2a3d6b69e7c6b4e73607d34a5abffa41f49bb1e58bb63ae869200ac2086648673</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s10958-023-06681-x$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s10958-023-06681-x$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>315,781,785,27926,27927,41490,42559,51321</link.rule.ids></links><search><creatorcontrib>Derkachev, S. E.</creatorcontrib><creatorcontrib>Ivanov, A. V.</creatorcontrib><title>Racah Coefficients for the Group SL(2,ℝ)</title><title>Journal of mathematical sciences (New York, N.Y.)</title><addtitle>J Math Sci</addtitle><description>The paper is devoted to the derivation of a universal integral representation for 6
j
-symbols, or Racah coefficients, for the tensor product of three unitary representations of the principle series of the group SL(2, ℝ). The problem of calculating 6
j
-symbols admits a natural reformulation in the language of Feynman diagrams. The original diagram can be significantly simplified and reduced to a basic diagram using the Gorishnii–Isaev method. In the case of representations of the principle series, we obtained a closed expression in the form of the Mellin–Barnes integral for the basic diagram.</description><subject>Feynman diagrams</subject><subject>Mathematical analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Principles</subject><subject>Representations</subject><subject>Symbols</subject><subject>Tensors</subject><issn>1072-3374</issn><issn>1573-8795</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kc9KAzEQhxdRsFZfwNOCFyum5s9ukj1K0VooCK2eQzadbLe0uzXZQr37Gr6cT2J0hVIoksOE4ftmYH5RdElwn2As7jzBWSoRpgxhziVB26OoQ1LBkBRZehz-WFDEmEhOozPvFzhIXLJOdDPRRs_jQQ3WlqaEqvGxrV3czCEeunqzjqfja3r79fHZO49OrF56uPir3ej18eFl8ITGz8PR4H6MDONyi6hmM57zDITheQKCcSxmLNGpzq3VCbFJlucEUpnnnGmQPKMYa0Ox5DyRXLBudNXOXbv6bQO-UYt646qwUlEpRBIQnuyoQi9BlZWtG6fNqvRG3QtBMsJESgOFDlAFVOD0sq7AlqG9x_cP8OHNYFWag0JvTwhMA9um0Bvv1Wg62WdpyxpXe-_AqrUrV9q9K4LVT4yqjVGFGNVvjGobJNZKPsBVAW53jX-sb0NFm44</recordid><startdate>20230904</startdate><enddate>20230904</enddate><creator>Derkachev, S. E.</creator><creator>Ivanov, A. V.</creator><general>Springer International Publishing</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>ISR</scope></search><sort><creationdate>20230904</creationdate><title>Racah Coefficients for the Group SL(2,ℝ)</title><author>Derkachev, S. E. ; Ivanov, A. V.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c368x-2a3d6b69e7c6b4e73607d34a5abffa41f49bb1e58bb63ae869200ac2086648673</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Feynman diagrams</topic><topic>Mathematical analysis</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Principles</topic><topic>Representations</topic><topic>Symbols</topic><topic>Tensors</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Derkachev, S. E.</creatorcontrib><creatorcontrib>Ivanov, A. V.</creatorcontrib><collection>CrossRef</collection><collection>Gale In Context: Science</collection><jtitle>Journal of mathematical sciences (New York, N.Y.)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Derkachev, S. E.</au><au>Ivanov, A. V.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Racah Coefficients for the Group SL(2,ℝ)</atitle><jtitle>Journal of mathematical sciences (New York, N.Y.)</jtitle><stitle>J Math Sci</stitle><date>2023-09-04</date><risdate>2023</risdate><volume>275</volume><issue>3</issue><spage>289</spage><epage>298</epage><pages>289-298</pages><issn>1072-3374</issn><eissn>1573-8795</eissn><abstract>The paper is devoted to the derivation of a universal integral representation for 6
j
-symbols, or Racah coefficients, for the tensor product of three unitary representations of the principle series of the group SL(2, ℝ). The problem of calculating 6
j
-symbols admits a natural reformulation in the language of Feynman diagrams. The original diagram can be significantly simplified and reduced to a basic diagram using the Gorishnii–Isaev method. In the case of representations of the principle series, we obtained a closed expression in the form of the Mellin–Barnes integral for the basic diagram.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s10958-023-06681-x</doi><tpages>10</tpages><oa>free_for_read</oa></addata></record> |
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| source | SpringerNature Journals |
| subjects | Feynman diagrams Mathematical analysis Mathematics Mathematics and Statistics Principles Representations Symbols Tensors |
| title | Racah Coefficients for the Group SL(2,ℝ) |
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