{"title":"时间有序积和指数","authors":"C. Lam","doi":"10.1201/9781003078296-27","DOIUrl":null,"url":null,"abstract":"I discuss a formula decomposing the integral of time-ordered products of operators into sums of products of integrals of time-ordered commutators. The resulting factorization enables summation of an infinite series to be carried out to yield an explicit formula for the time-ordered exponentials. The Campbell-Baker-Hausdorff formula and the nonabelian eikonal formula obtained previously are both special cases of this result.","PeriodicalId":409936,"journal":{"name":"Mathematical Methods of Quantum Physics","volume":"38 8","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1998-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Time-Ordered Products and Exponentials\",\"authors\":\"C. Lam\",\"doi\":\"10.1201/9781003078296-27\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"I discuss a formula decomposing the integral of time-ordered products of operators into sums of products of integrals of time-ordered commutators. The resulting factorization enables summation of an infinite series to be carried out to yield an explicit formula for the time-ordered exponentials. The Campbell-Baker-Hausdorff formula and the nonabelian eikonal formula obtained previously are both special cases of this result.\",\"PeriodicalId\":409936,\"journal\":{\"name\":\"Mathematical Methods of Quantum Physics\",\"volume\":\"38 8\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1998-05-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Methods of Quantum Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1201/9781003078296-27\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Methods of Quantum Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1201/9781003078296-27","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
I discuss a formula decomposing the integral of time-ordered products of operators into sums of products of integrals of time-ordered commutators. The resulting factorization enables summation of an infinite series to be carried out to yield an explicit formula for the time-ordered exponentials. The Campbell-Baker-Hausdorff formula and the nonabelian eikonal formula obtained previously are both special cases of this result.
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