{"title":"A one-parameter family of approximations of the solution of the initial Cauchy problem for the Dirac equation","authors":"C. Corona","doi":"10.1088/0305-4470/22/13/028","DOIUrl":null,"url":null,"abstract":"A one-parameter family of approximations of the initial Cauchy problem for the Dirac equation in (3+1) spacetime dimensions is given. The approximation is defined in terms of the mean translation operator G(t,y)f=(4 pi rho )-1 A integral mod nu mod = rho gf(y-tv) d nu S. The family is indexed by the 'speed' rho . The main result is that the approximation converges to the solution (in the L2-norm) if rho >or= square root 3c,c being the speed of light.","PeriodicalId":16785,"journal":{"name":"Journal of Physics A","volume":"195 6","pages":"2341-2353"},"PeriodicalIF":0.0000,"publicationDate":"1989-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Physics A","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1088/0305-4470/22/13/028","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
A one-parameter family of approximations of the initial Cauchy problem for the Dirac equation in (3+1) spacetime dimensions is given. The approximation is defined in terms of the mean translation operator G(t,y)f=(4 pi rho )-1 A integral mod nu mod = rho gf(y-tv) d nu S. The family is indexed by the 'speed' rho . The main result is that the approximation converges to the solution (in the L2-norm) if rho >or= square root 3c,c being the speed of light.
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