{"title":"具有最大总占据特性的广义玻色子和费米子算子","authors":"N I Stoilova and J Van der Jeugt","doi":"10.1088/1751-8121/ad77fd","DOIUrl":null,"url":null,"abstract":"We propose a new generalization of the standard (anti-)commutation relations for creation and annihilation operators of bosons and fermions. These relations preserve the usual symmetry properties of bosons and fermions. Only the standard (anti-)commutator relation involving one creation and one annihilation operator is deformed by introducing fractional coefficients, containing a positive integer parameter p. The Fock space is determined by the classical definition. The new relations are chosen in such a way that the total occupation number in the system has the maximum value p. From the actions of creation and annihilation operators in the Fock space, a group theoretical framework is determined, and from here the correspondence with known particle statistics is established.","PeriodicalId":16763,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"10 1","pages":""},"PeriodicalIF":2.0000,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Generalized boson and fermion operators with a maximal total occupation property\",\"authors\":\"N I Stoilova and J Van der Jeugt\",\"doi\":\"10.1088/1751-8121/ad77fd\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We propose a new generalization of the standard (anti-)commutation relations for creation and annihilation operators of bosons and fermions. These relations preserve the usual symmetry properties of bosons and fermions. Only the standard (anti-)commutator relation involving one creation and one annihilation operator is deformed by introducing fractional coefficients, containing a positive integer parameter p. The Fock space is determined by the classical definition. The new relations are chosen in such a way that the total occupation number in the system has the maximum value p. From the actions of creation and annihilation operators in the Fock space, a group theoretical framework is determined, and from here the correspondence with known particle statistics is established.\",\"PeriodicalId\":16763,\"journal\":{\"name\":\"Journal of Physics A: Mathematical and Theoretical\",\"volume\":\"10 1\",\"pages\":\"\"},\"PeriodicalIF\":2.0000,\"publicationDate\":\"2024-09-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Physics A: Mathematical and Theoretical\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1088/1751-8121/ad77fd\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Physics A: Mathematical and Theoretical","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1751-8121/ad77fd","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
Generalized boson and fermion operators with a maximal total occupation property
We propose a new generalization of the standard (anti-)commutation relations for creation and annihilation operators of bosons and fermions. These relations preserve the usual symmetry properties of bosons and fermions. Only the standard (anti-)commutator relation involving one creation and one annihilation operator is deformed by introducing fractional coefficients, containing a positive integer parameter p. The Fock space is determined by the classical definition. The new relations are chosen in such a way that the total occupation number in the system has the maximum value p. From the actions of creation and annihilation operators in the Fock space, a group theoretical framework is determined, and from here the correspondence with known particle statistics is established.
期刊介绍:
Publishing 50 issues a year, Journal of Physics A: Mathematical and Theoretical is a major journal of theoretical physics reporting research on the mathematical structures that describe fundamental processes of the physical world and on the analytical, computational and numerical methods for exploring these structures.