{"title":"Sl (6, r)为非相对论性量子系统的对称群","authors":"E. Ifidon, E. Oghre","doi":"10.4314/GJMAS.V3I1.21349","DOIUrl":null,"url":null,"abstract":"It is shown that the 13 one parameter generators of the Lie group SL(6, R) are the maximal group of symmetries for nonrelativistic quantum systems. The group action on the set of states S Ĥ (H complex Hilbert space) preserves transition probabilities as well as the dynamics of the system. By considering a prolongation of the group action on Ĥ, we have a generalized rotation of state vectors in which the norms are preserved. Thus one obtains new symmetries as well as new representations which aid in the simplification of the system. New solutions can thus be obtained, which in most cases have realistic physical properties. KEY WORDS: Prolongations, Symmetry Groups, Sets of States. Global Jnl of Mathematical Sciences Vol. 31) 2004: 35-46","PeriodicalId":126381,"journal":{"name":"Global Journal of Mathematical Sciences","volume":"56 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2004-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"SL (6,R) AS THE GROUP OF SYMMETRIES FOR NON RELATIVISTIC QUANTUM SYSTEMS\",\"authors\":\"E. Ifidon, E. Oghre\",\"doi\":\"10.4314/GJMAS.V3I1.21349\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"It is shown that the 13 one parameter generators of the Lie group SL(6, R) are the maximal group of symmetries for nonrelativistic quantum systems. The group action on the set of states S Ĥ (H complex Hilbert space) preserves transition probabilities as well as the dynamics of the system. By considering a prolongation of the group action on Ĥ, we have a generalized rotation of state vectors in which the norms are preserved. Thus one obtains new symmetries as well as new representations which aid in the simplification of the system. New solutions can thus be obtained, which in most cases have realistic physical properties. KEY WORDS: Prolongations, Symmetry Groups, Sets of States. Global Jnl of Mathematical Sciences Vol. 31) 2004: 35-46\",\"PeriodicalId\":126381,\"journal\":{\"name\":\"Global Journal of Mathematical Sciences\",\"volume\":\"56 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2004-05-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Global Journal of Mathematical Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4314/GJMAS.V3I1.21349\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Global Journal of Mathematical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4314/GJMAS.V3I1.21349","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
SL (6,R) AS THE GROUP OF SYMMETRIES FOR NON RELATIVISTIC QUANTUM SYSTEMS
It is shown that the 13 one parameter generators of the Lie group SL(6, R) are the maximal group of symmetries for nonrelativistic quantum systems. The group action on the set of states S Ĥ (H complex Hilbert space) preserves transition probabilities as well as the dynamics of the system. By considering a prolongation of the group action on Ĥ, we have a generalized rotation of state vectors in which the norms are preserved. Thus one obtains new symmetries as well as new representations which aid in the simplification of the system. New solutions can thus be obtained, which in most cases have realistic physical properties. KEY WORDS: Prolongations, Symmetry Groups, Sets of States. Global Jnl of Mathematical Sciences Vol. 31) 2004: 35-46
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
