{"title":"关于哈密顿不稳定性的Ostrogradsky定理","authors":"R. Woodard","doi":"10.4249/scholarpedia.32243","DOIUrl":null,"url":null,"abstract":"Ostrogradsky's construction of a Hamiltonian formalism for nondegenerate higher derivative Lagrangians is reviewed. The resulting instability imposes by far the most powerful restriction on fundamental, interacting, continuum Lagrangian field theories. A discussion is given of the problems raised by attempts to evade this restriction.","PeriodicalId":74760,"journal":{"name":"Scholarpedia journal","volume":"10 1","pages":"32243"},"PeriodicalIF":0.0000,"publicationDate":"2015-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"431","resultStr":"{\"title\":\"Ostrogradsky's theorem on Hamiltonian instability\",\"authors\":\"R. Woodard\",\"doi\":\"10.4249/scholarpedia.32243\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Ostrogradsky's construction of a Hamiltonian formalism for nondegenerate higher derivative Lagrangians is reviewed. The resulting instability imposes by far the most powerful restriction on fundamental, interacting, continuum Lagrangian field theories. A discussion is given of the problems raised by attempts to evade this restriction.\",\"PeriodicalId\":74760,\"journal\":{\"name\":\"Scholarpedia journal\",\"volume\":\"10 1\",\"pages\":\"32243\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-06-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"431\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Scholarpedia journal\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4249/scholarpedia.32243\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Scholarpedia journal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4249/scholarpedia.32243","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Ostrogradsky's construction of a Hamiltonian formalism for nondegenerate higher derivative Lagrangians is reviewed. The resulting instability imposes by far the most powerful restriction on fundamental, interacting, continuum Lagrangian field theories. A discussion is given of the problems raised by attempts to evade this restriction.
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