{"title":"环量子引力中的宇宙学:保持规范自由度的对称约简","authors":"Matteo Bruno","doi":"10.1088/1361-6382/ae0088","DOIUrl":null,"url":null,"abstract":"In this manuscript, we address the issue of the loss of SU(2) internal symmetry in loop quantum cosmology and its relationship with loop quantum gravity. Drawing inspiration from Yang–Mills theory and employing the framework of fiber bundle theory, we propose a new gauge-invariant symmetry-reduction approach. Using this method, we successfully identify a cosmological sector of general relativity in terms of Ashtekar variables that preserves the SU(2) structure of the theory as well as part of the diffeomorphism gauge symmetry. Additionally, we analyze the properties of cylindrical functions and the classical constraint algebra, revealing that certain cylindrical functions exhibit distinctive symmetry features.","PeriodicalId":10282,"journal":{"name":"Classical and Quantum Gravity","volume":"46 1","pages":""},"PeriodicalIF":3.7000,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Cosmology in loop quantum gravity: symmetry reduction preserving gauge degrees of freedom\",\"authors\":\"Matteo Bruno\",\"doi\":\"10.1088/1361-6382/ae0088\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this manuscript, we address the issue of the loss of SU(2) internal symmetry in loop quantum cosmology and its relationship with loop quantum gravity. Drawing inspiration from Yang–Mills theory and employing the framework of fiber bundle theory, we propose a new gauge-invariant symmetry-reduction approach. Using this method, we successfully identify a cosmological sector of general relativity in terms of Ashtekar variables that preserves the SU(2) structure of the theory as well as part of the diffeomorphism gauge symmetry. Additionally, we analyze the properties of cylindrical functions and the classical constraint algebra, revealing that certain cylindrical functions exhibit distinctive symmetry features.\",\"PeriodicalId\":10282,\"journal\":{\"name\":\"Classical and Quantum Gravity\",\"volume\":\"46 1\",\"pages\":\"\"},\"PeriodicalIF\":3.7000,\"publicationDate\":\"2025-09-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Classical and Quantum Gravity\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1088/1361-6382/ae0088\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ASTRONOMY & ASTROPHYSICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Classical and Quantum Gravity","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1361-6382/ae0088","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
Cosmology in loop quantum gravity: symmetry reduction preserving gauge degrees of freedom
In this manuscript, we address the issue of the loss of SU(2) internal symmetry in loop quantum cosmology and its relationship with loop quantum gravity. Drawing inspiration from Yang–Mills theory and employing the framework of fiber bundle theory, we propose a new gauge-invariant symmetry-reduction approach. Using this method, we successfully identify a cosmological sector of general relativity in terms of Ashtekar variables that preserves the SU(2) structure of the theory as well as part of the diffeomorphism gauge symmetry. Additionally, we analyze the properties of cylindrical functions and the classical constraint algebra, revealing that certain cylindrical functions exhibit distinctive symmetry features.
期刊介绍:
Classical and Quantum Gravity is an established journal for physicists, mathematicians and cosmologists in the fields of gravitation and the theory of spacetime. The journal is now the acknowledged world leader in classical relativity and all areas of quantum gravity.