[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-264858-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-264858-en":131},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","revisiting-the-symmetries-of-galilean-electrodynamics","Revisiting the Symmetries of Galilean Electrodynamics","","We determine the symmetries of four related non-relativistic field theories: Galilean Electrodynamics (GED), GED with five free static scalar fields, Galilean Yang-Mills (GYM), and GYM with five interacting scalar fields. The work corrects prior results by showing that GED in d+1 dimensions possesses an infinite-dimensional symmetry algebra. In 3+1 dimensions, the symmetries realize the conformal Milne algebra extended by a spatial dilatation generator Dx. The paper also explains how these findings fit the non-relativistic AdS5/CFT4 correspondence framework.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & Report",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/revisiting-the-symmetries-of-galilean-electrodynamics/264858/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/revisiting-the-symmetries-of-galilean-electrodynamics/264858.png","ImageObject",300,407,{"name":42,"@type":43},"Rhys","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-01","2026-09-14",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",13,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What theories and extensions does the paper analyze?","Question",{"text":63,"@type":64},"It studies Galilean Electrodynamics (GED) and Galilean Yang-Mills (GYM), including GED with five free static scalars and GYM with five interacting (adjoint) scalar fields.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"What correction to earlier literature does the paper provide for GED symmetries?",{"text":68,"@type":64},"It corrects previous claims by finding that GED in generic spacetime dimension d+1 always has infinitely many symmetries, rather than a finite set in the off-shell analysis.",{"name":70,"@type":61,"acceptedAnswer":71},"How do the 3+1 dimensional symmetries relate to conformal structures?",{"text":72,"@type":64},"In 3+1 dimensions, the GED symmetries correspond to the conformal Milne algebra extended by an additional spatial dilatation generator called Dx.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},264858,1789390677,{"code":4,"msg":82,"data":83},"success",[84,88,92,96,101,106,111,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":93,"show_sort_weight":94,"slug":95},"Exam",70,"exam",{"id":97,"doc_module":4,"doc_module_name":25,"category_name":98,"show_sort_weight":99,"slug":100},5,"Comic",60,"comic",{"id":102,"doc_module":4,"doc_module_name":25,"category_name":103,"show_sort_weight":104,"slug":105},6,"Technology",50,"technology",{"id":107,"doc_module":4,"doc_module_name":25,"category_name":108,"show_sort_weight":109,"slug":110},7,"Healthcare",40,"healthcare",{"id":112,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":113,"slug":114},8,30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":25,"category_name":129,"show_sort_weight":97,"slug":130},19,"General","general",{"code":4,"msg":82,"data":132},{"doc_id":79,"user_id":133,"nickname":42,"user_avatar":134,"doc_module":4,"category_id":112,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":55,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":80,"read_time":144,"preview_page_count":4},687207024643,"https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2","arXiv :2411 . 192 17v4 [hep-th] 6 Jun 2025  \nZMP-HH/24-29  \nRevisiting the Symmetries of Galilean Electrodynamics  \nAndrea FontanellaRe and Juan Miguel Nieto GarcíaIm  \nRe School of Mathematics & Hamilton Mathematics Institute,  \nTrinity College Dublin, Ireland  \nandrea .fontanella[at][tcd.ie](tcd.ie)  \nIm II. Institut für Theoretische Physik, Universität Hamburg,  \nLuruper Chaussee 149, 22761 Hamburg, Germany  \njuan.miguel.nieto.garcia[at]desy.de  \nAbstract  \nWe determine the symmetries of four different theories: I) Galilean Electrodynamics (GED), II) GED coupled to 5 free static scalar fields, III) Galilean Yang-Mills (GYM), and IV) GYM coupled to 5 interacting scalar fields. We correct some old results in the literature, by finding that the symmetries of GED in a spacetime of generic dimension d + 1 is always infinite dimensional, and in 3 + 1 they correspond to the conformal Milne algebra extended by a spatial dilatation generator, which we call Dx. Finally, we comment on how these results fit into the framework of thenon-relativistic AdS5 /CFT4 correspondence.  \nContents  \n1 Symmetries of the GED action 2  \n2 Symmetries of the GED action with 5 free static scalars 5  \n3 Symmetries of the GYM action 6  \n4 Symmetries of the GYM action with 5 adjoint scalars 8  \n5 An application to the non-relativistic AdS5 /CFT4 correspondence 10  \n6 Conclusions 10  \nIntroduction  \nGalilean Electrodynamics (GED) is a very important and simple theory, so that it maybe regarded as the “hydrogen atom” of non-relativistic field theories. This theory was first proposed in [1] as a Lagrangian formulation for the electric and magnetic non-relativistic limits of the Maxwell’s equations proposed by Le Bellac and Lévy-Leblond in [2], as Galilean invariant equations of electromagnetisms. Later, GED was also derived as anon-relativistic limit of the Maxwell theory with an additional scalar field [3] . The nonabelian generalisation, called Galilean Yang-Mills (GYM), was proposed in [4] . Both GED and GYM theories, opportunely supplemented by five additional scalar fields, also appear when considering the gauge theory dual of the GGK non-relativistic string theory with target space the String Newton-Cartan version of AdS5 ×S5 [5–7] . The study of thenon-relativistic AdS/CFT correspondence is currently a growing field, see [8–11] for other recent work on the subject.  \nRegarding the identification of the symmetries of GED, there has been some confusion in the past, which we wish to clarify in this article. Symmetries of the GED theory have been analysed in [12], and they have been distinguished between symmetries of the equations of motion (named “on-shell”) and symmetries of the action (named “offshell”) . The on-shell symmetries were found to be infinitely many, with the peculiarity that in 3+1 dimensions they contain a finite truncation of the Galilean Conformal Algebra (GCA) . On the other hand, the off-shell symmetries were found to be finite, and with the property of containing only a Lifshitz scale invariance instead of the finite truncation of the GCA. However, the reason for finding only a finite amount of off-shell symmetries can be traced back to the fact that in [12] the Lagrangian was demanded to transform under the symmetries as a total derivative of a specific type, namely δL = ∂µ (ξµ L), instead of transforming as δL = ∂µ Fµ , where Fµ is a generic function of fields, coordinates  \nand parameters, and ξµ is a vector field containing the transformation parameters. As it is standard practice in QFT, any boundary term generated by the symmetry can be eliminated by imposing suitable boundary conditions, e.g. the fall-off condition on the fields at infinite spatial distance.  \nIn the more recent paper [13], the symmetries of the GED and GYM theories were considered again. In 2+1 dimensions, they found that they are infinitely many, and we do match their result. However, in 3+1 dimensions, i.e. the case relevant for holography, they obtain that","cbCaiushjoP877UG","https://ap.wps.com/l/cbCaiushjoP877UG","pdf",586928,"English","# Abstract\n# Introduction\n# 1 Symmetries of the GED action\n## 2 Symmetries of the GED action with 5 free static scalars\n## 3 Symmetries of the GYM action\n## 4 Symmetries of the GYM action with 5 adjoint scalars\n## 5 An application to the non-relativistic AdS5/CFT4 correspondence\n## 6 Conclusions","[{\"question\":\"What theories and extensions does the paper analyze?\",\"answer\":\"It studies Galilean Electrodynamics (GED) and Galilean Yang-Mills (GYM), including GED with five free static scalars and GYM with five interacting (adjoint) scalar fields.\"},{\"question\":\"What correction to earlier literature does the paper provide for GED symmetries?\",\"answer\":\"It corrects previous claims by finding that GED in generic spacetime dimension d+1 always has infinitely many symmetries, rather than a finite set in the off-shell analysis.\"},{\"question\":\"How do the 3+1 dimensional symmetries relate to conformal structures?\",\"answer\":\"In 3+1 dimensions, the GED symmetries correspond to the conformal Milne algebra extended by an additional spatial dilatation generator called Dx.\"}]","Revisiting the Symmetries of Galilean Electrodynamics | PDF",33]