Nonassociative Weyl star products
A bstract Deformation quantization is a formal deformation of the algebra of smooth functions on some manifold. In the classical setting, the Poisson bracket serves as an initial conditions, while the associativity allows to proceed to higher orders. Some applications to string theory require deform...
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| Veröffentlicht in: | The journal of high energy physics 2015-09, Vol.2015 (9), p.1-16, Article 103 |
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| container_title | The journal of high energy physics |
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| creator | Kupriyanov, V.G. Vassilevich, D.V. |
| description | A
bstract
Deformation quantization is a formal deformation of the algebra of smooth functions on some manifold. In the classical setting, the Poisson bracket serves as an initial conditions, while the associativity allows to proceed to higher orders. Some applications to string theory require deformation in the direction of a quasi-Poisson bracket (that does not satisfy the Jacobi identity). This initial condition is incompatible with associativity, it is quite unclear which restrictions can be imposed on the deformation. We show that for any quasi-Poisson bracket the deformation quantization exists and is essentially unique if one requires (weak) hermiticity and the Weyl condition. We also propose an iterative procedure that allows one to compute the star product up to any desired order. |
| doi_str_mv | 10.1007/JHEP09(2015)103 |
| format | Article |
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bstract
Deformation quantization is a formal deformation of the algebra of smooth functions on some manifold. In the classical setting, the Poisson bracket serves as an initial conditions, while the associativity allows to proceed to higher orders. Some applications to string theory require deformation in the direction of a quasi-Poisson bracket (that does not satisfy the Jacobi identity). This initial condition is incompatible with associativity, it is quite unclear which restrictions can be imposed on the deformation. We show that for any quasi-Poisson bracket the deformation quantization exists and is essentially unique if one requires (weak) hermiticity and the Weyl condition. We also propose an iterative procedure that allows one to compute the star product up to any desired order.</description><identifier>ISSN: 1029-8479</identifier><identifier>EISSN: 1029-8479</identifier><identifier>DOI: 10.1007/JHEP09(2015)103</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Algebra ; Brackets ; Classical and Quantum Gravitation ; Deformation ; Elementary Particles ; High energy physics ; Initial conditions ; Manifolds ; Mathematical analysis ; Physics ; Physics and Astronomy ; Quantization ; Quantum Field Theories ; Quantum Field Theory ; Quantum Physics ; Regular Article - Theoretical Physics ; Relativity Theory ; Stars ; String Theory</subject><ispartof>The journal of high energy physics, 2015-09, Vol.2015 (9), p.1-16, Article 103</ispartof><rights>The Author(s) 2015</rights><rights>SISSA, Trieste, Italy 2015</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c430t-ce3c18f3456590fd54ca7af3ab246833633bd5ee59a2511d75bea479f42a87ae3</citedby><cites>FETCH-LOGICAL-c430t-ce3c18f3456590fd54ca7af3ab246833633bd5ee59a2511d75bea479f42a87ae3</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/JHEP09(2015)103$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://doi.org/10.1007/JHEP09(2015)103$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>315,781,785,865,27929,27930,41125,42194,51581</link.rule.ids></links><search><creatorcontrib>Kupriyanov, V.G.</creatorcontrib><creatorcontrib>Vassilevich, D.V.</creatorcontrib><title>Nonassociative Weyl star products</title><title>The journal of high energy physics</title><addtitle>J. High Energ. Phys</addtitle><description>A
bstract
Deformation quantization is a formal deformation of the algebra of smooth functions on some manifold. In the classical setting, the Poisson bracket serves as an initial conditions, while the associativity allows to proceed to higher orders. Some applications to string theory require deformation in the direction of a quasi-Poisson bracket (that does not satisfy the Jacobi identity). This initial condition is incompatible with associativity, it is quite unclear which restrictions can be imposed on the deformation. We show that for any quasi-Poisson bracket the deformation quantization exists and is essentially unique if one requires (weak) hermiticity and the Weyl condition. We also propose an iterative procedure that allows one to compute the star product up to any desired order.</description><subject>Algebra</subject><subject>Brackets</subject><subject>Classical and Quantum Gravitation</subject><subject>Deformation</subject><subject>Elementary Particles</subject><subject>High energy physics</subject><subject>Initial conditions</subject><subject>Manifolds</subject><subject>Mathematical analysis</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantization</subject><subject>Quantum Field Theories</subject><subject>Quantum Field Theory</subject><subject>Quantum Physics</subject><subject>Regular Article - Theoretical Physics</subject><subject>Relativity Theory</subject><subject>Stars</subject><subject>String Theory</subject><issn>1029-8479</issn><issn>1029-8479</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNp1kEFLAzEQhYMoWKtnrxUv9bB2ZidpNkcp1SpFPSgeQ5rNypbtbk12hf57U9ZDETzNMHzvzeMxdolwiwBy8rSYv4Iap4DiBoGO2AAhVUnGpTo-2E_ZWQhriBQqGLCr56Y2ITS2NG357UYfbleNQmv8aOubvLNtOGcnhamCu_idQ_Z-P3-bLZLly8Pj7G6ZWE7QJtaRxawgLqZCQZELbo00BZlVyqcZ0ZRolQvnhDKpQMylWDkT8xQ8NZk0joZs3PvGx1-dC63elMG6qjK1a7qgMYMMkRSoiF7_QddN5-uYTqNEkgRc8khNesr6JgTvCr315cb4nUbQ-8p0X5neVxYPFBXQK0Ik60_nD3z_kfwA2WprrQ</recordid><startdate>20150901</startdate><enddate>20150901</enddate><creator>Kupriyanov, V.G.</creator><creator>Vassilevich, D.V.</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</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>HCIFZ</scope><scope>P5Z</scope><scope>P62</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope></search><sort><creationdate>20150901</creationdate><title>Nonassociative Weyl star products</title><author>Kupriyanov, V.G. ; Vassilevich, D.V.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c430t-ce3c18f3456590fd54ca7af3ab246833633bd5ee59a2511d75bea479f42a87ae3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Algebra</topic><topic>Brackets</topic><topic>Classical and Quantum Gravitation</topic><topic>Deformation</topic><topic>Elementary Particles</topic><topic>High energy physics</topic><topic>Initial conditions</topic><topic>Manifolds</topic><topic>Mathematical analysis</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantization</topic><topic>Quantum Field Theories</topic><topic>Quantum Field Theory</topic><topic>Quantum Physics</topic><topic>Regular Article - Theoretical Physics</topic><topic>Relativity Theory</topic><topic>Stars</topic><topic>String Theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Kupriyanov, V.G.</creatorcontrib><creatorcontrib>Vassilevich, D.V.</creatorcontrib><collection>Springer Nature OA/Free Journals</collection><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & 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><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>The journal of high energy physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Kupriyanov, V.G.</au><au>Vassilevich, D.V.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Nonassociative Weyl star products</atitle><jtitle>The journal of high energy physics</jtitle><stitle>J. High Energ. Phys</stitle><date>2015-09-01</date><risdate>2015</risdate><volume>2015</volume><issue>9</issue><spage>1</spage><epage>16</epage><pages>1-16</pages><artnum>103</artnum><issn>1029-8479</issn><eissn>1029-8479</eissn><abstract>A
bstract
Deformation quantization is a formal deformation of the algebra of smooth functions on some manifold. In the classical setting, the Poisson bracket serves as an initial conditions, while the associativity allows to proceed to higher orders. Some applications to string theory require deformation in the direction of a quasi-Poisson bracket (that does not satisfy the Jacobi identity). This initial condition is incompatible with associativity, it is quite unclear which restrictions can be imposed on the deformation. We show that for any quasi-Poisson bracket the deformation quantization exists and is essentially unique if one requires (weak) hermiticity and the Weyl condition. We also propose an iterative procedure that allows one to compute the star product up to any desired order.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/JHEP09(2015)103</doi><tpages>16</tpages><oa>free_for_read</oa></addata></record> |
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| source | DOAJ Directory of Open Access Journals; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; Alma/SFX Local Collection; Springer Nature OA/Free Journals |
| subjects | Algebra Brackets Classical and Quantum Gravitation Deformation Elementary Particles High energy physics Initial conditions Manifolds Mathematical analysis Physics Physics and Astronomy Quantization Quantum Field Theories Quantum Field Theory Quantum Physics Regular Article - Theoretical Physics Relativity Theory Stars String Theory |
| title | Nonassociative Weyl star products |
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