{"title":"模块化的类别","authors":"Michael Mueger","doi":"10.1093/acprof:oso/9780199646296.003.0006","DOIUrl":null,"url":null,"abstract":"• Modular categories serve as input datum for the Reshetikhin-Turaev construction of topological quantum field theories in 2+1 dimensions and therefore give rise to invariants of smooth 3-manifolds. This goes some way towards making Witten’s interpretation of the Jones polynomial via Chern-Simons QFT rigorous. (But since there still is no complete rigorous non-perturbative construction of the Chern-Simons QFTs by conventional quantum field theory methods, there also is no proof of their equivalence to the RT-TQFTs constructed using the representation theory of quantum groups.)","PeriodicalId":273067,"journal":{"name":"Quantum Physics and Linguistics","volume":"22 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2012-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"30","resultStr":"{\"title\":\"Modular Categories\",\"authors\":\"Michael Mueger\",\"doi\":\"10.1093/acprof:oso/9780199646296.003.0006\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"• Modular categories serve as input datum for the Reshetikhin-Turaev construction of topological quantum field theories in 2+1 dimensions and therefore give rise to invariants of smooth 3-manifolds. This goes some way towards making Witten’s interpretation of the Jones polynomial via Chern-Simons QFT rigorous. (But since there still is no complete rigorous non-perturbative construction of the Chern-Simons QFTs by conventional quantum field theory methods, there also is no proof of their equivalence to the RT-TQFTs constructed using the representation theory of quantum groups.)\",\"PeriodicalId\":273067,\"journal\":{\"name\":\"Quantum Physics and Linguistics\",\"volume\":\"22 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-01-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"30\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quantum Physics and Linguistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1093/acprof:oso/9780199646296.003.0006\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quantum Physics and Linguistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1093/acprof:oso/9780199646296.003.0006","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
• Modular categories serve as input datum for the Reshetikhin-Turaev construction of topological quantum field theories in 2+1 dimensions and therefore give rise to invariants of smooth 3-manifolds. This goes some way towards making Witten’s interpretation of the Jones polynomial via Chern-Simons QFT rigorous. (But since there still is no complete rigorous non-perturbative construction of the Chern-Simons QFTs by conventional quantum field theory methods, there also is no proof of their equivalence to the RT-TQFTs constructed using the representation theory of quantum groups.)
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