{"title":"Lagrangian mechanics for fields","authors":"A. Steane","doi":"10.1093/oso/9780192895646.003.0028","DOIUrl":null,"url":null,"abstract":"An introduction to Lagrangian methods for classical fields in flat spacetime and then in curved spacetime. The Euler-Lagrange equations for Lagrangian densities are obtained, and applied to the wave, Klein-Gordan, Weyl, Dirac, Maxwell and Proca equations. The canonical energy tensor is obtained. Conservation laws and Noether’s theorem are described. An example of the treatment of Interactions is given by presenting the the QED Lagrangian. Finally, covariant Lagrangian methods are described, and the Einstein field eqution is derived from the Einstein-Hilbert action.","PeriodicalId":365636,"journal":{"name":"Relativity Made Relatively Easy Volume 2","volume":"81 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Relativity Made Relatively Easy Volume 2","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1093/oso/9780192895646.003.0028","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
An introduction to Lagrangian methods for classical fields in flat spacetime and then in curved spacetime. The Euler-Lagrange equations for Lagrangian densities are obtained, and applied to the wave, Klein-Gordan, Weyl, Dirac, Maxwell and Proca equations. The canonical energy tensor is obtained. Conservation laws and Noether’s theorem are described. An example of the treatment of Interactions is given by presenting the the QED Lagrangian. Finally, covariant Lagrangian methods are described, and the Einstein field eqution is derived from the Einstein-Hilbert action.
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