Multivector Contractions Revisited, Part II
The theory of contractions of multivectors, and star duality, was reorganized in a previous article, and here we present some applications. First, we study inner and outer spaces associated to a general multivector M via the equations v ∧ M = 0 and v ⌟ M = 0 . They are then used to analyze special d...
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| creator | Mandolesi, André L. G. |
| description | The theory of contractions of multivectors, and star duality, was reorganized in a previous article, and here we present some applications. First, we study inner and outer spaces associated to a general multivector
M
via the equations
v
∧
M
=
0
and
v
⌟
M
=
0
. They are then used to analyze special decompositions, factorizations and ‘carvings’ of
M
, to define generalized grades, and to obtain new simplicity criteria, including a reduced set of Plücker-like relations. We also discuss how contractions are related to supersymmetry, and give formulas for supercommutators of multi-fermion creation and annihilation operators. |
| doi_str_mv | 10.1007/s00006-024-01358-3 |
| format | Article |
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M
via the equations
v
∧
M
=
0
and
v
⌟
M
=
0
. They are then used to analyze special decompositions, factorizations and ‘carvings’ of
M
, to define generalized grades, and to obtain new simplicity criteria, including a reduced set of Plücker-like relations. We also discuss how contractions are related to supersymmetry, and give formulas for supercommutators of multi-fermion creation and annihilation operators.</description><identifier>ISSN: 0188-7009</identifier><identifier>EISSN: 1661-4909</identifier><identifier>DOI: 10.1007/s00006-024-01358-3</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Applications of Mathematics ; Fermions ; Mathematical and Computational Physics ; Mathematical Methods in Physics ; Physics ; Physics and Astronomy ; Supersymmetry ; Theoretical</subject><ispartof>Advances in applied Clifford algebras, 2024-11, Vol.34 (5), Article 54</ispartof><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. 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><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c200t-c3598dd8eb4c239c53bb4a13c4a853a849645ec7750b486a3884cfea7a2aff13</cites><orcidid>0000-0002-5329-7034</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00006-024-01358-3$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00006-024-01358-3$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,777,781,27905,27906,41469,42538,51300</link.rule.ids></links><search><creatorcontrib>Mandolesi, André L. G.</creatorcontrib><title>Multivector Contractions Revisited, Part II</title><title>Advances in applied Clifford algebras</title><addtitle>Adv. Appl. Clifford Algebras</addtitle><description>The theory of contractions of multivectors, and star duality, was reorganized in a previous article, and here we present some applications. First, we study inner and outer spaces associated to a general multivector
M
via the equations
v
∧
M
=
0
and
v
⌟
M
=
0
. They are then used to analyze special decompositions, factorizations and ‘carvings’ of
M
, to define generalized grades, and to obtain new simplicity criteria, including a reduced set of Plücker-like relations. We also discuss how contractions are related to supersymmetry, and give formulas for supercommutators of multi-fermion creation and annihilation operators.</description><subject>Applications of Mathematics</subject><subject>Fermions</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematical Methods in Physics</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Supersymmetry</subject><subject>Theoretical</subject><issn>0188-7009</issn><issn>1661-4909</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LxDAURYMoWEf_gKuCS42-9CVpupTix8CIIrMPaZpKh7Edk3TAf2-0gjvf5m7uuQ8OIecMrhlAeRMgnaRQcAoMhaJ4QDImJaO8guqQZMCUoiVAdUxOQtgAcImoMnL5NG1jv3c2jj6vxyF6Y2M_DiF_dfs-9NG1V_mL8TFfLk_JUWe2wZ395oKs7-_W9SNdPT8s69sVtQVApBZFpdpWuYbbAisrsGm4YWi5UQKN4pXkwtmyFNBwJQ0qxW3nTGkK03UMF-Rint358WNyIerNOPkhfdTImOKyBOSpVcwt68cQvOv0zvfvxn9qBvrbiZ6d6ORE_zjRmCCcoZDKw5vzf9P_UF8Oh2K8</recordid><startdate>20241101</startdate><enddate>20241101</enddate><creator>Mandolesi, André L. G.</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-5329-7034</orcidid></search><sort><creationdate>20241101</creationdate><title>Multivector Contractions Revisited, Part II</title><author>Mandolesi, André L. G.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c200t-c3598dd8eb4c239c53bb4a13c4a853a849645ec7750b486a3884cfea7a2aff13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Applications of Mathematics</topic><topic>Fermions</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematical Methods in Physics</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Supersymmetry</topic><topic>Theoretical</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Mandolesi, André L. G.</creatorcontrib><collection>CrossRef</collection><jtitle>Advances in applied Clifford algebras</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Mandolesi, André L. G.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Multivector Contractions Revisited, Part II</atitle><jtitle>Advances in applied Clifford algebras</jtitle><stitle>Adv. Appl. Clifford Algebras</stitle><date>2024-11-01</date><risdate>2024</risdate><volume>34</volume><issue>5</issue><artnum>54</artnum><issn>0188-7009</issn><eissn>1661-4909</eissn><abstract>The theory of contractions of multivectors, and star duality, was reorganized in a previous article, and here we present some applications. First, we study inner and outer spaces associated to a general multivector
M
via the equations
v
∧
M
=
0
and
v
⌟
M
=
0
. They are then used to analyze special decompositions, factorizations and ‘carvings’ of
M
, to define generalized grades, and to obtain new simplicity criteria, including a reduced set of Plücker-like relations. We also discuss how contractions are related to supersymmetry, and give formulas for supercommutators of multi-fermion creation and annihilation operators.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00006-024-01358-3</doi><orcidid>https://orcid.org/0000-0002-5329-7034</orcidid></addata></record> |
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| subjects | Applications of Mathematics Fermions Mathematical and Computational Physics Mathematical Methods in Physics Physics Physics and Astronomy Supersymmetry Theoretical |
| title | Multivector Contractions Revisited, Part II |
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