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Operators for generic effective field theory at any dimension: on-shell amplitude basis construction
A bstract We describe a general procedure to construct the independent and complete operator bases for generic Lorentz invariant effective field theories, given any kind of gauge symmetry and field content, up to any mass dimension. By considering the operator as contact on-shell amplitude, the so-c...
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| Published in: | The journal of high energy physics 2022-04, Vol.2022 (4), p.140-89, Article 140 |
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| Main Authors: | , , , , |
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| cited_by | cdi_FETCH-LOGICAL-c417t-acd78fb6b5eb493c2c9cfac44a86055136151a47c18b8988590d0353a01237f73 |
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| cites | cdi_FETCH-LOGICAL-c417t-acd78fb6b5eb493c2c9cfac44a86055136151a47c18b8988590d0353a01237f73 |
| container_end_page | 89 |
| container_issue | 4 |
| container_start_page | 140 |
| container_title | The journal of high energy physics |
| container_volume | 2022 |
| creator | Li, Hao-Lin Ren, Zhe Xiao, Ming-Lei Yu, Jiang-Hao Zheng, Yu-Hui |
| description | A
bstract
We describe a general procedure to construct the independent and complete operator bases for generic Lorentz invariant effective field theories, given any kind of gauge symmetry and field content, up to any mass dimension. By considering the operator as contact on-shell amplitude, the so-called amplitude operator correspondence, we provide a unified construction of the Lorentz and gauge and flavor structures by Young Tableau tensor. Several bases are constructed to emphasize different aspects: independence (y-basis and m-basis), repeated fields with flavors (p-basis and f-basis), and conserved quantum numbers (j-basis). We also provide new algorithms for finding the m-basis by defining inner products for group factors and the p-basis by constructing the matrix representations of the Young symmetrizers from group generators. The on-shell amplitude basis gives us a systematic way to convert any operator into such basis, so that the conversions between any other operator bases can be easily done by linear algebra. All of these are implemented in a Mathematica package: ABC4EFT (
A
mplitude
B
asis
C
onstruction for
E
ffective
F
ield
T
heories). |
| doi_str_mv | 10.1007/JHEP04(2022)140 |
| format | article |
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bstract
We describe a general procedure to construct the independent and complete operator bases for generic Lorentz invariant effective field theories, given any kind of gauge symmetry and field content, up to any mass dimension. By considering the operator as contact on-shell amplitude, the so-called amplitude operator correspondence, we provide a unified construction of the Lorentz and gauge and flavor structures by Young Tableau tensor. Several bases are constructed to emphasize different aspects: independence (y-basis and m-basis), repeated fields with flavors (p-basis and f-basis), and conserved quantum numbers (j-basis). We also provide new algorithms for finding the m-basis by defining inner products for group factors and the p-basis by constructing the matrix representations of the Young symmetrizers from group generators. The on-shell amplitude basis gives us a systematic way to convert any operator into such basis, so that the conversions between any other operator bases can be easily done by linear algebra. All of these are implemented in a Mathematica package: ABC4EFT (
A
mplitude
B
asis
C
onstruction for
E
ffective
F
ield
T
heories).</description><identifier>ISSN: 1029-8479</identifier><identifier>EISSN: 1029-8479</identifier><identifier>DOI: 10.1007/JHEP04(2022)140</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Algorithms ; Amplitudes ; Classical and Quantum Gravitation ; Effective Field Theories ; Elementary Particles ; Field theory ; Flavor (particle physics) ; Group theory ; High energy physics ; Linear algebra ; Mathematical analysis ; Matrix representation ; Operators (mathematics) ; Physics ; Physics and Astronomy ; Quantum Field Theories ; Quantum Field Theory ; Quantum numbers ; Quantum Physics ; Regular Article - Theoretical Physics ; Relativity Theory ; Scattering Amplitudes ; SMEFT ; String Theory ; Tensors</subject><ispartof>The journal of high energy physics, 2022-04, Vol.2022 (4), p.140-89, Article 140</ispartof><rights>The Author(s) 2022</rights><rights>The Author(s) 2022. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c417t-acd78fb6b5eb493c2c9cfac44a86055136151a47c18b8988590d0353a01237f73</citedby><cites>FETCH-LOGICAL-c417t-acd78fb6b5eb493c2c9cfac44a86055136151a47c18b8988590d0353a01237f73</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.proquest.com/docview/2655930998/fulltextPDF?pq-origsite=primo$$EPDF$$P50$$Gproquest$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/2655930998?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,25752,27923,27924,37011,44589,74897</link.rule.ids></links><search><creatorcontrib>Li, Hao-Lin</creatorcontrib><creatorcontrib>Ren, Zhe</creatorcontrib><creatorcontrib>Xiao, Ming-Lei</creatorcontrib><creatorcontrib>Yu, Jiang-Hao</creatorcontrib><creatorcontrib>Zheng, Yu-Hui</creatorcontrib><title>Operators for generic effective field theory at any dimension: on-shell amplitude basis construction</title><title>The journal of high energy physics</title><addtitle>J. High Energ. Phys</addtitle><description>A
bstract
We describe a general procedure to construct the independent and complete operator bases for generic Lorentz invariant effective field theories, given any kind of gauge symmetry and field content, up to any mass dimension. By considering the operator as contact on-shell amplitude, the so-called amplitude operator correspondence, we provide a unified construction of the Lorentz and gauge and flavor structures by Young Tableau tensor. Several bases are constructed to emphasize different aspects: independence (y-basis and m-basis), repeated fields with flavors (p-basis and f-basis), and conserved quantum numbers (j-basis). We also provide new algorithms for finding the m-basis by defining inner products for group factors and the p-basis by constructing the matrix representations of the Young symmetrizers from group generators. The on-shell amplitude basis gives us a systematic way to convert any operator into such basis, so that the conversions between any other operator bases can be easily done by linear algebra. All of these are implemented in a Mathematica package: ABC4EFT (
A
mplitude
B
asis
C
onstruction for
E
ffective
F
ield
T
heories).</description><subject>Algorithms</subject><subject>Amplitudes</subject><subject>Classical and Quantum Gravitation</subject><subject>Effective Field Theories</subject><subject>Elementary Particles</subject><subject>Field theory</subject><subject>Flavor (particle physics)</subject><subject>Group theory</subject><subject>High energy physics</subject><subject>Linear algebra</subject><subject>Mathematical analysis</subject><subject>Matrix representation</subject><subject>Operators (mathematics)</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Field Theories</subject><subject>Quantum Field Theory</subject><subject>Quantum numbers</subject><subject>Quantum Physics</subject><subject>Regular Article - Theoretical Physics</subject><subject>Relativity Theory</subject><subject>Scattering Amplitudes</subject><subject>SMEFT</subject><subject>String Theory</subject><subject>Tensors</subject><issn>1029-8479</issn><issn>1029-8479</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><sourceid>DOA</sourceid><recordid>eNp1kUFv1DAQhSMEEqVw5mqJCxxCx4kd29xQVdqiSu2hnK2JM956lbUX21tp_z0pqYALpxmN3vvmSa9p3nP4zAHU2ferizsQHzvouk9cwIvmhENnWi2UefnP_rp5U8oWgEtu4KSZbveUsaZcmE-ZbShSDo6R9-RqeCTmA80Tqw-U8pFhZRiPbAo7iiWk-IWl2JYHmmeGu_0c6mEiNmIJhbkUS82HBZLi2-aVx7nQu-d52vz4dnF_ftXe3F5en3-9aZ3gqrboJqX9OIySRmF61znjPDohUA8gJe-HJTQK5bgetdFaGpiglz0C73rlVX_aXK_cKeHW7nPYYT7ahMH-PqS8sZhrcDNZAq3V0KMUBoU3UpMUTroOFUljpFhYH1bWPqefByrVbtMhxyW-7QYpTQ_G6EV1tqpcTqVk8n--crBPtdi1FvtUi11qWRywOsqijBvKf7n_s_wCkfKOxg</recordid><startdate>20220426</startdate><enddate>20220426</enddate><creator>Li, Hao-Lin</creator><creator>Ren, Zhe</creator><creator>Xiao, Ming-Lei</creator><creator>Yu, Jiang-Hao</creator><creator>Zheng, Yu-Hui</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><general>SpringerOpen</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>DOA</scope></search><sort><creationdate>20220426</creationdate><title>Operators for generic effective field theory at any dimension: on-shell amplitude basis construction</title><author>Li, Hao-Lin ; Ren, Zhe ; Xiao, Ming-Lei ; Yu, Jiang-Hao ; Zheng, Yu-Hui</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c417t-acd78fb6b5eb493c2c9cfac44a86055136151a47c18b8988590d0353a01237f73</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Algorithms</topic><topic>Amplitudes</topic><topic>Classical and Quantum Gravitation</topic><topic>Effective Field Theories</topic><topic>Elementary Particles</topic><topic>Field theory</topic><topic>Flavor (particle physics)</topic><topic>Group theory</topic><topic>High energy physics</topic><topic>Linear algebra</topic><topic>Mathematical analysis</topic><topic>Matrix representation</topic><topic>Operators (mathematics)</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum Field Theories</topic><topic>Quantum Field Theory</topic><topic>Quantum numbers</topic><topic>Quantum Physics</topic><topic>Regular Article - Theoretical Physics</topic><topic>Relativity Theory</topic><topic>Scattering Amplitudes</topic><topic>SMEFT</topic><topic>String Theory</topic><topic>Tensors</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Li, Hao-Lin</creatorcontrib><creatorcontrib>Ren, Zhe</creatorcontrib><creatorcontrib>Xiao, Ming-Lei</creatorcontrib><creatorcontrib>Yu, Jiang-Hao</creatorcontrib><creatorcontrib>Zheng, Yu-Hui</creatorcontrib><collection>SpringerOpen (Open Access)</collection><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</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>Directory of Open Access Journals (DOAJ)</collection><jtitle>The journal of high energy physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Li, Hao-Lin</au><au>Ren, Zhe</au><au>Xiao, Ming-Lei</au><au>Yu, Jiang-Hao</au><au>Zheng, Yu-Hui</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Operators for generic effective field theory at any dimension: on-shell amplitude basis construction</atitle><jtitle>The journal of high energy physics</jtitle><stitle>J. High Energ. Phys</stitle><date>2022-04-26</date><risdate>2022</risdate><volume>2022</volume><issue>4</issue><spage>140</spage><epage>89</epage><pages>140-89</pages><artnum>140</artnum><issn>1029-8479</issn><eissn>1029-8479</eissn><abstract>A
bstract
We describe a general procedure to construct the independent and complete operator bases for generic Lorentz invariant effective field theories, given any kind of gauge symmetry and field content, up to any mass dimension. By considering the operator as contact on-shell amplitude, the so-called amplitude operator correspondence, we provide a unified construction of the Lorentz and gauge and flavor structures by Young Tableau tensor. Several bases are constructed to emphasize different aspects: independence (y-basis and m-basis), repeated fields with flavors (p-basis and f-basis), and conserved quantum numbers (j-basis). We also provide new algorithms for finding the m-basis by defining inner products for group factors and the p-basis by constructing the matrix representations of the Young symmetrizers from group generators. The on-shell amplitude basis gives us a systematic way to convert any operator into such basis, so that the conversions between any other operator bases can be easily done by linear algebra. All of these are implemented in a Mathematica package: ABC4EFT (
A
mplitude
B
asis
C
onstruction for
E
ffective
F
ield
T
heories).</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/JHEP04(2022)140</doi><tpages>89</tpages><oa>free_for_read</oa></addata></record> |
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| subjects | Algorithms Amplitudes Classical and Quantum Gravitation Effective Field Theories Elementary Particles Field theory Flavor (particle physics) Group theory High energy physics Linear algebra Mathematical analysis Matrix representation Operators (mathematics) Physics Physics and Astronomy Quantum Field Theories Quantum Field Theory Quantum numbers Quantum Physics Regular Article - Theoretical Physics Relativity Theory Scattering Amplitudes SMEFT String Theory Tensors |
| title | Operators for generic effective field theory at any dimension: on-shell amplitude basis construction |
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