{"title":"Conserved currents from nonlocal constants in relativistic scalar field theories","authors":"Mattia Scomparin","doi":"10.1016/S0034-4877(23)00040-X","DOIUrl":null,"url":null,"abstract":"<div><p><span>Nonlocal constants are functions that are constant along motion but whose value depends on the past history of the motion itself. They have been introduced to study ODEs<span> and, among all applications, they provide first integrals in special cases. In this respect, a new approach to get nonlocal constants within the framework of Lagrangian </span></span>scalar field theory is introduced. We derive locally-conserved currents from them, and we prove the consistency of our results by recovering some standard Noetherian results. Applications include the real/complex nonlinear interacting theory and the real dissipative Klein–Gordon theory.</p></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"91 3","pages":"Pages 359-377"},"PeriodicalIF":1.0000,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Reports on Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S003448772300040X","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 1
Abstract
Nonlocal constants are functions that are constant along motion but whose value depends on the past history of the motion itself. They have been introduced to study ODEs and, among all applications, they provide first integrals in special cases. In this respect, a new approach to get nonlocal constants within the framework of Lagrangian scalar field theory is introduced. We derive locally-conserved currents from them, and we prove the consistency of our results by recovering some standard Noetherian results. Applications include the real/complex nonlinear interacting theory and the real dissipative Klein–Gordon theory.
期刊介绍:
Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.