{"title":"Symmetry transformations of extremals and higher conserved quantities: Invariant Yang–Mills connections","authors":"Luca Accornero, M. Palese","doi":"10.1063/5.0038533","DOIUrl":null,"url":null,"abstract":"We characterize symmetry transformations of Lagrangian extremals generating `on shell' conservation laws. We relate symmetry transformations of extremals to Jacobi fields and study symmetries of higher variations by proving that a pair given by a symmetry of the $l$-th variation of a Lagrangian and by a Jacobi field of the $s$-th variation of the same Lagrangian (with $s<l$) is associated with an `of shell' conserved current. The conserved current associated with two symmetry transformations is constructed and, as a case of study, its expression for invariant Yang--Mills connections on Minkowski space-times is obtained.","PeriodicalId":8469,"journal":{"name":"arXiv: Mathematical Physics","volume":"18 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Mathematical Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1063/5.0038533","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3
Abstract
We characterize symmetry transformations of Lagrangian extremals generating `on shell' conservation laws. We relate symmetry transformations of extremals to Jacobi fields and study symmetries of higher variations by proving that a pair given by a symmetry of the $l$-th variation of a Lagrangian and by a Jacobi field of the $s$-th variation of the same Lagrangian (with $s
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