{"title":"广义相对论","authors":"J. Allday","doi":"10.1201/9781315165141-8","DOIUrl":null,"url":null,"abstract":"G L, where L is a 4-form called Lagrange density. In electrodynamics, it is given by L := − 2 dA ∧ ? dA + A ∧ J. Now consider an infinitesimal variation of the electromagnetic field byA→ A+ Q, where Q is a 1-form and where 0 < 1 is small. The principle of least action tells us that S does not change to lowest order in , provided that Q vanishes on the boundary ∂G. (a) Show that the stationarity of S leads us to the condition (2P) ∫","PeriodicalId":179016,"journal":{"name":"Space-time","volume":"42 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Theory of General Relativity\",\"authors\":\"J. Allday\",\"doi\":\"10.1201/9781315165141-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"G L, where L is a 4-form called Lagrange density. In electrodynamics, it is given by L := − 2 dA ∧ ? dA + A ∧ J. Now consider an infinitesimal variation of the electromagnetic field byA→ A+ Q, where Q is a 1-form and where 0 < 1 is small. The principle of least action tells us that S does not change to lowest order in , provided that Q vanishes on the boundary ∂G. (a) Show that the stationarity of S leads us to the condition (2P) ∫\",\"PeriodicalId\":179016,\"journal\":{\"name\":\"Space-time\",\"volume\":\"42 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-05-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Space-time\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1201/9781315165141-8\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Space-time","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1201/9781315165141-8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
G L，其中L是4形式的拉格朗日密度。在电动力学中，它由L:=−2 dA∧?dA + A∧J.现在考虑A→A+ Q对电磁场的无穷小变化，其中Q是1形式，且0 < 1很小。最小作用原理告诉我们，如果Q在边界∂G上消失，S不会改变到最低阶。(a)证明S的平稳性使我们得到条件(2P)∫
G L, where L is a 4-form called Lagrange density. In electrodynamics, it is given by L := − 2 dA ∧ ? dA + A ∧ J. Now consider an infinitesimal variation of the electromagnetic field byA→ A+ Q, where Q is a 1-form and where 0 < 1 is small. The principle of least action tells us that S does not change to lowest order in , provided that Q vanishes on the boundary ∂G. (a) Show that the stationarity of S leads us to the condition (2P) ∫
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