{"title":"量子引力可量子化几何的必要性","authors":"Abhishek Kumar Mehta","doi":"10.1088/1361-6382/ad4fda","DOIUrl":null,"url":null,"abstract":"\n In this paper, Dirac Quantization of $3D$ gravity in the first-order formalism is attempted where instead of quantizing the connection and triad fields, the connection and the triad 1-forms themselves are quantized. The exterior derivative operator on the space of differential forms is treated as the `time' derivative to compute the momenta conjugate to these 1-forms. This manner of quantization allows one to compute the transition amplitude in $3D$ gravity which has a close, but not exact, match with the transition amplitude computed via LQG techniques. This inconsistency is interpreted as being due to the non-quantizable nature of differential geometry.","PeriodicalId":10282,"journal":{"name":"Classical and Quantum Gravity","volume":null,"pages":null},"PeriodicalIF":3.6000,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Necessity of quantizable geometry for quantum gravity\",\"authors\":\"Abhishek Kumar Mehta\",\"doi\":\"10.1088/1361-6382/ad4fda\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n In this paper, Dirac Quantization of $3D$ gravity in the first-order formalism is attempted where instead of quantizing the connection and triad fields, the connection and the triad 1-forms themselves are quantized. The exterior derivative operator on the space of differential forms is treated as the `time' derivative to compute the momenta conjugate to these 1-forms. This manner of quantization allows one to compute the transition amplitude in $3D$ gravity which has a close, but not exact, match with the transition amplitude computed via LQG techniques. This inconsistency is interpreted as being due to the non-quantizable nature of differential geometry.\",\"PeriodicalId\":10282,\"journal\":{\"name\":\"Classical and Quantum Gravity\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.6000,\"publicationDate\":\"2024-05-23\",\"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/ad4fda\",\"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/ad4fda","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}
Necessity of quantizable geometry for quantum gravity
In this paper, Dirac Quantization of $3D$ gravity in the first-order formalism is attempted where instead of quantizing the connection and triad fields, the connection and the triad 1-forms themselves are quantized. The exterior derivative operator on the space of differential forms is treated as the `time' derivative to compute the momenta conjugate to these 1-forms. This manner of quantization allows one to compute the transition amplitude in $3D$ gravity which has a close, but not exact, match with the transition amplitude computed via LQG techniques. This inconsistency is interpreted as being due to the non-quantizable nature of differential geometry.
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.