Dimensional reduction of the Dirac theory
We perform a reduction from three to two spatial dimensions of the physics of a spin- 1 2 fermion coupled to the electromagnetic (EM) field, by applying Hadamard’s method of descent. We consider first the free case, in which motion is determined by the Dirac equation, and then the coupling with a dy...
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| Veröffentlicht in: | Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2023-02, Vol.56 (6), p.65201 |
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| container_title | Journal of physics. A, Mathematical and theoretical |
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| creator | Angelone, Giuliano Ercolessi, Elisa Facchi, Paolo Lonigro, Davide Maggi, Rocco Marmo, Giuseppe Pascazio, Saverio Pepe, Francesco V |
| description | We perform a reduction from three to two spatial dimensions of the physics of a spin-
1
2
fermion coupled to the electromagnetic (EM) field, by applying Hadamard’s method of descent. We consider first the free case, in which motion is determined by the Dirac equation, and then the coupling with a dynamical EM field, governed by the Dirac–Maxwell equations. We find that invariance along one spatial direction splits the free Dirac equation in two decoupled theories. On the other hand, a dimensional reduction in the presence of an EM field provides a more complicated theory in
2
+
1
dimensions, in which the method of decent is extended by using the covariant derivative. Equations simplify, but decoupling between different physical sectors occurs only if specific classes of solutions are considered. |
| doi_str_mv | 10.1088/1751-8121/acb869 |
| format | Article |
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1
2
fermion coupled to the electromagnetic (EM) field, by applying Hadamard’s method of descent. We consider first the free case, in which motion is determined by the Dirac equation, and then the coupling with a dynamical EM field, governed by the Dirac–Maxwell equations. We find that invariance along one spatial direction splits the free Dirac equation in two decoupled theories. On the other hand, a dimensional reduction in the presence of an EM field provides a more complicated theory in
2
+
1
dimensions, in which the method of decent is extended by using the covariant derivative. Equations simplify, but decoupling between different physical sectors occurs only if specific classes of solutions are considered.</description><identifier>ISSN: 1751-8113</identifier><identifier>EISSN: 1751-8121</identifier><identifier>DOI: 10.1088/1751-8121/acb869</identifier><identifier>CODEN: JPHAC5</identifier><language>eng</language><publisher>IOP Publishing</publisher><subject>dimensional reduction ; Dirac equation ; Dirac–Maxwell equation ; Hadamard’s descent ; low-dimensional theories</subject><ispartof>Journal of physics. A, Mathematical and theoretical, 2023-02, Vol.56 (6), p.65201</ispartof><rights>2023 The Author(s). Published by IOP Publishing Ltd</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c322t-47f33a75ea03ac3e9e64e59bd58de3a6320f3c1e307d338650178ad3b729b3573</citedby><cites>FETCH-LOGICAL-c322t-47f33a75ea03ac3e9e64e59bd58de3a6320f3c1e307d338650178ad3b729b3573</cites><orcidid>0000-0002-0733-3380 ; 0000-0002-0792-8122 ; 0000-0002-7214-5685 ; 0000-0003-2662-2193 ; 0000-0002-7407-063X ; 0000-0001-9152-6515</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://iopscience.iop.org/article/10.1088/1751-8121/acb869/pdf$$EPDF$$P50$$Giop$$Hfree_for_read</linktopdf><link.rule.ids>314,776,780,27901,27902,53821,53868</link.rule.ids></links><search><creatorcontrib>Angelone, Giuliano</creatorcontrib><creatorcontrib>Ercolessi, Elisa</creatorcontrib><creatorcontrib>Facchi, Paolo</creatorcontrib><creatorcontrib>Lonigro, Davide</creatorcontrib><creatorcontrib>Maggi, Rocco</creatorcontrib><creatorcontrib>Marmo, Giuseppe</creatorcontrib><creatorcontrib>Pascazio, Saverio</creatorcontrib><creatorcontrib>Pepe, Francesco V</creatorcontrib><title>Dimensional reduction of the Dirac theory</title><title>Journal of physics. A, Mathematical and theoretical</title><addtitle>JPhysA</addtitle><addtitle>J. Phys. A: Math. Theor</addtitle><description>We perform a reduction from three to two spatial dimensions of the physics of a spin-
1
2
fermion coupled to the electromagnetic (EM) field, by applying Hadamard’s method of descent. We consider first the free case, in which motion is determined by the Dirac equation, and then the coupling with a dynamical EM field, governed by the Dirac–Maxwell equations. We find that invariance along one spatial direction splits the free Dirac equation in two decoupled theories. On the other hand, a dimensional reduction in the presence of an EM field provides a more complicated theory in
2
+
1
dimensions, in which the method of decent is extended by using the covariant derivative. Equations simplify, but decoupling between different physical sectors occurs only if specific classes of solutions are considered.</description><subject>dimensional reduction</subject><subject>Dirac equation</subject><subject>Dirac–Maxwell equation</subject><subject>Hadamard’s descent</subject><subject>low-dimensional theories</subject><issn>1751-8113</issn><issn>1751-8121</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>O3W</sourceid><recordid>eNp1j79rwzAQhUVpoWnavaPXQt2cdJYljSXpLwh0aWchS2fqkERBcob897VxydbpPo73HnyM3XN44qD1givJS80FXzjf6NpcsNn5dXlmjtfsJucNgKzAiBl7WHU72ucu7t22SBSOvh-4iG3R_1Cx6pLzI8V0umVXrdtmuvu7c_b9-vK1fC_Xn28fy-d16VGIvqxUi-iUJAfoPJKhuiJpmiB1IHQ1CmjRc0JQAVHXErjSLmCjhGlQKpwzmHZ9ijknau0hdTuXTpaDHVXt6GJHLzupDpXHqdLFg93EYxpk8v_xXzSWU5Y</recordid><startdate>20230210</startdate><enddate>20230210</enddate><creator>Angelone, Giuliano</creator><creator>Ercolessi, Elisa</creator><creator>Facchi, Paolo</creator><creator>Lonigro, Davide</creator><creator>Maggi, Rocco</creator><creator>Marmo, Giuseppe</creator><creator>Pascazio, Saverio</creator><creator>Pepe, Francesco V</creator><general>IOP Publishing</general><scope>O3W</scope><scope>TSCCA</scope><scope>AAYXX</scope><scope>CITATION</scope><orcidid>https://orcid.org/0000-0002-0733-3380</orcidid><orcidid>https://orcid.org/0000-0002-0792-8122</orcidid><orcidid>https://orcid.org/0000-0002-7214-5685</orcidid><orcidid>https://orcid.org/0000-0003-2662-2193</orcidid><orcidid>https://orcid.org/0000-0002-7407-063X</orcidid><orcidid>https://orcid.org/0000-0001-9152-6515</orcidid></search><sort><creationdate>20230210</creationdate><title>Dimensional reduction of the Dirac theory</title><author>Angelone, Giuliano ; Ercolessi, Elisa ; Facchi, Paolo ; Lonigro, Davide ; Maggi, Rocco ; Marmo, Giuseppe ; Pascazio, Saverio ; Pepe, Francesco V</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c322t-47f33a75ea03ac3e9e64e59bd58de3a6320f3c1e307d338650178ad3b729b3573</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>dimensional reduction</topic><topic>Dirac equation</topic><topic>Dirac–Maxwell equation</topic><topic>Hadamard’s descent</topic><topic>low-dimensional theories</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Angelone, Giuliano</creatorcontrib><creatorcontrib>Ercolessi, Elisa</creatorcontrib><creatorcontrib>Facchi, Paolo</creatorcontrib><creatorcontrib>Lonigro, Davide</creatorcontrib><creatorcontrib>Maggi, Rocco</creatorcontrib><creatorcontrib>Marmo, Giuseppe</creatorcontrib><creatorcontrib>Pascazio, Saverio</creatorcontrib><creatorcontrib>Pepe, Francesco V</creatorcontrib><collection>IOP Publishing Free Content</collection><collection>IOPscience (Open Access)</collection><collection>CrossRef</collection><jtitle>Journal of physics. A, Mathematical and theoretical</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Angelone, Giuliano</au><au>Ercolessi, Elisa</au><au>Facchi, Paolo</au><au>Lonigro, Davide</au><au>Maggi, Rocco</au><au>Marmo, Giuseppe</au><au>Pascazio, Saverio</au><au>Pepe, Francesco V</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Dimensional reduction of the Dirac theory</atitle><jtitle>Journal of physics. A, Mathematical and theoretical</jtitle><stitle>JPhysA</stitle><addtitle>J. Phys. A: Math. Theor</addtitle><date>2023-02-10</date><risdate>2023</risdate><volume>56</volume><issue>6</issue><spage>65201</spage><pages>65201-</pages><issn>1751-8113</issn><eissn>1751-8121</eissn><coden>JPHAC5</coden><abstract>We perform a reduction from three to two spatial dimensions of the physics of a spin-
1
2
fermion coupled to the electromagnetic (EM) field, by applying Hadamard’s method of descent. We consider first the free case, in which motion is determined by the Dirac equation, and then the coupling with a dynamical EM field, governed by the Dirac–Maxwell equations. We find that invariance along one spatial direction splits the free Dirac equation in two decoupled theories. On the other hand, a dimensional reduction in the presence of an EM field provides a more complicated theory in
2
+
1
dimensions, in which the method of decent is extended by using the covariant derivative. Equations simplify, but decoupling between different physical sectors occurs only if specific classes of solutions are considered.</abstract><pub>IOP Publishing</pub><doi>10.1088/1751-8121/acb869</doi><tpages>20</tpages><orcidid>https://orcid.org/0000-0002-0733-3380</orcidid><orcidid>https://orcid.org/0000-0002-0792-8122</orcidid><orcidid>https://orcid.org/0000-0002-7214-5685</orcidid><orcidid>https://orcid.org/0000-0003-2662-2193</orcidid><orcidid>https://orcid.org/0000-0002-7407-063X</orcidid><orcidid>https://orcid.org/0000-0001-9152-6515</orcidid><oa>free_for_read</oa></addata></record> |
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| language | eng |
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| source | IOP Publishing Journals; Institute of Physics (IOP) Journals - HEAL-Link |
| subjects | dimensional reduction Dirac equation Dirac–Maxwell equation Hadamard’s descent low-dimensional theories |
| title | Dimensional reduction of the Dirac theory |
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