{"title":"Non-factorizable separable systems and higher-order symmetries of the Dirac operator","authors":"M. Fels, N. Kamran","doi":"10.1098/rspa.1990.0032","DOIUrl":null,"url":null,"abstract":"It is shown that there exist separable systems for the Dirac operator on four-dimensional lorentzian spin manifolds that are not factorizable in the sense of Miller. The symmetry operators associated to these new separable systems are of higher order than the Dirac operator. They are characterized in the second-order case in terms of quadratic first integrals of the geodesic flow satisfying additional invariant conditions.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1990-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"27","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1098/rspa.1990.0032","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 27
Abstract
It is shown that there exist separable systems for the Dirac operator on four-dimensional lorentzian spin manifolds that are not factorizable in the sense of Miller. The symmetry operators associated to these new separable systems are of higher order than the Dirac operator. They are characterized in the second-order case in terms of quadratic first integrals of the geodesic flow satisfying additional invariant conditions.