Infinite-dimensional representations of the rotation group and Dirac monopole problem
Within the context of infinite-dimensional representations of the rotation group, the Dirac monopole problem is studied in detail. Irreducible infinite-dimensional representations, which have been realized in the indefinite metric Hilbert space, are given by linear unbounded operators in infinite-di...
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| Veröffentlicht in: | Journal of mathematical physics 2008-01, Vol.49 (1), p.013505-013505-26 |
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| container_end_page | 013505-26 |
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| container_issue | 1 |
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| container_title | Journal of mathematical physics |
| container_volume | 49 |
| creator | Nesterov, Alexander I. Aceves de la Cruz, Fermín |
| description | Within the context of infinite-dimensional representations of the rotation group, the Dirac monopole problem is studied in detail. Irreducible infinite-dimensional representations, which have been realized in the indefinite metric Hilbert space, are given by linear unbounded operators in infinite-dimensional topological spaces, supplied with a weak topology and associated weak convergence. We argue that an arbitrary magnetic charge is allowed, and the Dirac quantization condition can be replaced by a generalized quantization rule yielding a new quantum number, the so-called topological spin, which is related to the weight of the Dirac string. |
| doi_str_mv | 10.1063/1.2830430 |
| format | Article |
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Irreducible infinite-dimensional representations, which have been realized in the indefinite metric Hilbert space, are given by linear unbounded operators in infinite-dimensional topological spaces, supplied with a weak topology and associated weak convergence. We argue that an arbitrary magnetic charge is allowed, and the Dirac quantization condition can be replaced by a generalized quantization rule yielding a new quantum number, the so-called topological spin, which is related to the weight of the Dirac string.</description><identifier>ISSN: 0022-2488</identifier><identifier>EISSN: 1089-7658</identifier><identifier>DOI: 10.1063/1.2830430</identifier><identifier>CODEN: JMAPAQ</identifier><language>eng</language><publisher>Melville, NY: American Institute of Physics</publisher><subject>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS ; CONVERGENCE ; EIGENFUNCTIONS ; EIGENVALUES ; Euclidean space ; Exact sciences and technology ; GROUP THEORY ; HILBERT SPACE ; MAGNETIC MONOPOLES ; Mathematical methods in physics ; Mathematical problems ; Mathematics ; Physics ; QUANTIZATION ; Quantum theory ; ROTATION ; SCHROEDINGER EQUATION ; Sciences and techniques of general use ; SPIN ; TOPOLOGY</subject><ispartof>Journal of mathematical physics, 2008-01, Vol.49 (1), p.013505-013505-26</ispartof><rights>American Institute of Physics</rights><rights>2008 American Institute of Physics</rights><rights>2008 INIST-CNRS</rights><rights>Copyright American Institute of Physics Jan 2008</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c439t-d95dc1ac48a49a2498e89c6024c14d3aae30788cac49802910cef5a014c3b08b3</citedby><cites>FETCH-LOGICAL-c439t-d95dc1ac48a49a2498e89c6024c14d3aae30788cac49802910cef5a014c3b08b3</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/10.1063/1.2830430$$EHTML$$P50$$Gscitation$$H</linktohtml><link.rule.ids>230,314,780,784,794,885,1558,4509,27922,27923,76154,76160</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=20077776$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttps://www.osti.gov/biblio/21013809$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>Nesterov, Alexander I.</creatorcontrib><creatorcontrib>Aceves de la Cruz, Fermín</creatorcontrib><title>Infinite-dimensional representations of the rotation group and Dirac monopole problem</title><title>Journal of mathematical physics</title><description>Within the context of infinite-dimensional representations of the rotation group, the Dirac monopole problem is studied in detail. Irreducible infinite-dimensional representations, which have been realized in the indefinite metric Hilbert space, are given by linear unbounded operators in infinite-dimensional topological spaces, supplied with a weak topology and associated weak convergence. We argue that an arbitrary magnetic charge is allowed, and the Dirac quantization condition can be replaced by a generalized quantization rule yielding a new quantum number, the so-called topological spin, which is related to the weight of the Dirac string.</description><subject>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS</subject><subject>CONVERGENCE</subject><subject>EIGENFUNCTIONS</subject><subject>EIGENVALUES</subject><subject>Euclidean space</subject><subject>Exact sciences and technology</subject><subject>GROUP THEORY</subject><subject>HILBERT SPACE</subject><subject>MAGNETIC MONOPOLES</subject><subject>Mathematical methods in physics</subject><subject>Mathematical problems</subject><subject>Mathematics</subject><subject>Physics</subject><subject>QUANTIZATION</subject><subject>Quantum theory</subject><subject>ROTATION</subject><subject>SCHROEDINGER EQUATION</subject><subject>Sciences and techniques of general use</subject><subject>SPIN</subject><subject>TOPOLOGY</subject><issn>0022-2488</issn><issn>1089-7658</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2008</creationdate><recordtype>article</recordtype><recordid>eNp9kUlLBDEQhYMoOC4H_0FQPCi0VpbpqVwEGVcQvOg5ZNJpbelJ2qRH8N8b7XEB0boUFF896r0iZIfBEYNSHLMjjgKkgBUyYoCqmJRjXCUjAM4LLhHXyUZKTwCMoZQjcn_t68Y3vSuqZu58aoI3LY2uiy4535s-DxINNe0fHY1hGNCHGBYdNb6iZ000ls6DD11oHe1imLVuvkXWatMmt73sm-T-4vxuelXc3F5eT09vCiuF6otKjSvLjJVopDJcKnSobAlcWiYrYYwTMEG0mVAIXDGwrh4bYNKKGeBMbJK9QTekvtHJZh_20Qbvne01Z8AEgsrU7kDl654XLvX6KSxi9pkyMy4ZIvIMHQyQjSGl6GrdxWZu4qtmoN-j1Uwvo83s_lLQJGvaOhpvm_S1wAEmucrMnQzc-2Ufyf0t-vkH_eMPWeDwL4GXEL-XdVfV_8G_LbwBD9Kpeg</recordid><startdate>20080101</startdate><enddate>20080101</enddate><creator>Nesterov, Alexander I.</creator><creator>Aceves de la Cruz, Fermín</creator><general>American Institute of Physics</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>JQ2</scope><scope>L7M</scope><scope>OTOTI</scope></search><sort><creationdate>20080101</creationdate><title>Infinite-dimensional representations of the rotation group and Dirac monopole problem</title><author>Nesterov, Alexander I. ; Aceves de la Cruz, Fermín</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c439t-d95dc1ac48a49a2498e89c6024c14d3aae30788cac49802910cef5a014c3b08b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2008</creationdate><topic>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS</topic><topic>CONVERGENCE</topic><topic>EIGENFUNCTIONS</topic><topic>EIGENVALUES</topic><topic>Euclidean space</topic><topic>Exact sciences and technology</topic><topic>GROUP THEORY</topic><topic>HILBERT SPACE</topic><topic>MAGNETIC MONOPOLES</topic><topic>Mathematical methods in physics</topic><topic>Mathematical problems</topic><topic>Mathematics</topic><topic>Physics</topic><topic>QUANTIZATION</topic><topic>Quantum theory</topic><topic>ROTATION</topic><topic>SCHROEDINGER EQUATION</topic><topic>Sciences and techniques of general use</topic><topic>SPIN</topic><topic>TOPOLOGY</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Nesterov, Alexander I.</creatorcontrib><creatorcontrib>Aceves de la Cruz, Fermín</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>OSTI.GOV</collection><jtitle>Journal of mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Nesterov, Alexander I.</au><au>Aceves de la Cruz, Fermín</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Infinite-dimensional representations of the rotation group and Dirac monopole problem</atitle><jtitle>Journal of mathematical physics</jtitle><date>2008-01-01</date><risdate>2008</risdate><volume>49</volume><issue>1</issue><spage>013505</spage><epage>013505-26</epage><pages>013505-013505-26</pages><issn>0022-2488</issn><eissn>1089-7658</eissn><coden>JMAPAQ</coden><abstract>Within the context of infinite-dimensional representations of the rotation group, the Dirac monopole problem is studied in detail. Irreducible infinite-dimensional representations, which have been realized in the indefinite metric Hilbert space, are given by linear unbounded operators in infinite-dimensional topological spaces, supplied with a weak topology and associated weak convergence. We argue that an arbitrary magnetic charge is allowed, and the Dirac quantization condition can be replaced by a generalized quantization rule yielding a new quantum number, the so-called topological spin, which is related to the weight of the Dirac string.</abstract><cop>Melville, NY</cop><pub>American Institute of Physics</pub><doi>10.1063/1.2830430</doi><tpages>26</tpages></addata></record> |
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| ispartof | Journal of mathematical physics, 2008-01, Vol.49 (1), p.013505-013505-26 |
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| source | AIP Journals Complete; AIP Digital Archive |
| subjects | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS CONVERGENCE EIGENFUNCTIONS EIGENVALUES Euclidean space Exact sciences and technology GROUP THEORY HILBERT SPACE MAGNETIC MONOPOLES Mathematical methods in physics Mathematical problems Mathematics Physics QUANTIZATION Quantum theory ROTATION SCHROEDINGER EQUATION Sciences and techniques of general use SPIN TOPOLOGY |
| title | Infinite-dimensional representations of the rotation group and Dirac monopole problem |
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