{"title":"模糊球卡卢扎-克莱因模型中的费米子","authors":"Chengcheng Liu, Shahn Majid","doi":"arxiv-2409.06668","DOIUrl":null,"url":null,"abstract":"We consider spinors on the total space of a Kaluza-Klein model with fuzzy\nsphere fibre and geometrically realised Dirac operator on the product. We show\nthat a single massless spinor on the product appears on spacetime as multiplets\nof spinors with a particular signature of differing masses and $SU(2)$\nYang-Mills charges. For example, for the reduced fuzzy sphere isomorphic to\n$M_2(\\mathbb{C})$, a massless spinor appears as two $SU(2)$ doublets and an\n$SU(2)$ quadruplet in mass ratios $1:5/3:7/3$. Although such signatures do not\nappear to exactly math the Standard Model, the paper provides proof of concept\nof the approach, which can be applied to other noncommutative fibre algebras.","PeriodicalId":501339,"journal":{"name":"arXiv - PHYS - High Energy Physics - Theory","volume":"86 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fermions in the fuzzy sphere Kaluza-Klein model\",\"authors\":\"Chengcheng Liu, Shahn Majid\",\"doi\":\"arxiv-2409.06668\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider spinors on the total space of a Kaluza-Klein model with fuzzy\\nsphere fibre and geometrically realised Dirac operator on the product. We show\\nthat a single massless spinor on the product appears on spacetime as multiplets\\nof spinors with a particular signature of differing masses and $SU(2)$\\nYang-Mills charges. For example, for the reduced fuzzy sphere isomorphic to\\n$M_2(\\\\mathbb{C})$, a massless spinor appears as two $SU(2)$ doublets and an\\n$SU(2)$ quadruplet in mass ratios $1:5/3:7/3$. Although such signatures do not\\nappear to exactly math the Standard Model, the paper provides proof of concept\\nof the approach, which can be applied to other noncommutative fibre algebras.\",\"PeriodicalId\":501339,\"journal\":{\"name\":\"arXiv - PHYS - High Energy Physics - Theory\",\"volume\":\"86 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - PHYS - High Energy Physics - Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.06668\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - High Energy Physics - Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.06668","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We consider spinors on the total space of a Kaluza-Klein model with fuzzy
sphere fibre and geometrically realised Dirac operator on the product. We show
that a single massless spinor on the product appears on spacetime as multiplets
of spinors with a particular signature of differing masses and $SU(2)$
Yang-Mills charges. For example, for the reduced fuzzy sphere isomorphic to
$M_2(\mathbb{C})$, a massless spinor appears as two $SU(2)$ doublets and an
$SU(2)$ quadruplet in mass ratios $1:5/3:7/3$. Although such signatures do not
appear to exactly math the Standard Model, the paper provides proof of concept
of the approach, which can be applied to other noncommutative fibre algebras.