{"title":"具有第一积分的无散度场的整体对称性的存在性","authors":"D. Perrella, Nathan Duignan, David Pfefferl'e","doi":"10.1063/5.0152213","DOIUrl":null,"url":null,"abstract":"The relationship between symmetry fields and first integrals of divergence-free vector fields is explored in three dimensions in light of its relevance to plasma physics and magnetic confinement fusion. A Noether-type theorem is known: for each such symmetry, there corresponds a first integral. The extent to which the converse is true is investigated. In doing so, a reformulation of this Noether-type theorem is found for which the converse holds on what is called the toroidal region. Some consequences of the methods presented are quick proofs of the existence of flux coordinates for magnetic fields in high generality, without needing to assume a symmetry such as in the cases of magneto-hydrostatics or quasi-symmetry.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"27 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2023-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Existence of global symmetries of divergence-free fields with first integrals\",\"authors\":\"D. Perrella, Nathan Duignan, David Pfefferl'e\",\"doi\":\"10.1063/5.0152213\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The relationship between symmetry fields and first integrals of divergence-free vector fields is explored in three dimensions in light of its relevance to plasma physics and magnetic confinement fusion. A Noether-type theorem is known: for each such symmetry, there corresponds a first integral. The extent to which the converse is true is investigated. In doing so, a reformulation of this Noether-type theorem is found for which the converse holds on what is called the toroidal region. Some consequences of the methods presented are quick proofs of the existence of flux coordinates for magnetic fields in high generality, without needing to assume a symmetry such as in the cases of magneto-hydrostatics or quasi-symmetry.\",\"PeriodicalId\":50141,\"journal\":{\"name\":\"Journal of Mathematical Physics Analysis Geometry\",\"volume\":\"27 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-03-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Physics Analysis Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1063/5.0152213\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Physics Analysis Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1063/5.0152213","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Existence of global symmetries of divergence-free fields with first integrals
The relationship between symmetry fields and first integrals of divergence-free vector fields is explored in three dimensions in light of its relevance to plasma physics and magnetic confinement fusion. A Noether-type theorem is known: for each such symmetry, there corresponds a first integral. The extent to which the converse is true is investigated. In doing so, a reformulation of this Noether-type theorem is found for which the converse holds on what is called the toroidal region. Some consequences of the methods presented are quick proofs of the existence of flux coordinates for magnetic fields in high generality, without needing to assume a symmetry such as in the cases of magneto-hydrostatics or quasi-symmetry.
期刊介绍:
Journal of Mathematical Physics, Analysis, Geometry (JMPAG) publishes original papers and reviews on the main subjects:
mathematical problems of modern physics;
complex analysis and its applications;
asymptotic problems of differential equations;
spectral theory including inverse problems and their applications;
geometry in large and differential geometry;
functional analysis, theory of representations, and operator algebras including ergodic theory.
The Journal aims at a broad readership of actively involved in scientific research and/or teaching at all levels scientists.