{"title":"论量子力学中的非交换几何","authors":"Ilyas Haouam","doi":"10.30970/jps.24.2002","DOIUrl":null,"url":null,"abstract":"In this paper, we presented and reviewed a formalism that plays a central role in most of the investigations concerning noncommutative geometry. We presented existing methods that successfully allow us to utilize and apply the noncommutativity of phase-space in both quantum mechanics and quantum (cid:28)eld theory. In particular, we brie(cid:29)y explained the Weyl quantization, the Moyal(cid:21)Weyl product, the Bopp-shift transformations, and the Seiberg(cid:21)Witten maps.","PeriodicalId":43482,"journal":{"name":"Journal of Physical Studies","volume":"98 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"12","resultStr":"{\"title\":\"On the noncommutative geometry in quantum mechanics\",\"authors\":\"Ilyas Haouam\",\"doi\":\"10.30970/jps.24.2002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we presented and reviewed a formalism that plays a central role in most of the investigations concerning noncommutative geometry. We presented existing methods that successfully allow us to utilize and apply the noncommutativity of phase-space in both quantum mechanics and quantum (cid:28)eld theory. In particular, we brie(cid:29)y explained the Weyl quantization, the Moyal(cid:21)Weyl product, the Bopp-shift transformations, and the Seiberg(cid:21)Witten maps.\",\"PeriodicalId\":43482,\"journal\":{\"name\":\"Journal of Physical Studies\",\"volume\":\"98 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2020-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"12\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Physical Studies\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.30970/jps.24.2002\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Physical Studies","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.30970/jps.24.2002","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
On the noncommutative geometry in quantum mechanics
In this paper, we presented and reviewed a formalism that plays a central role in most of the investigations concerning noncommutative geometry. We presented existing methods that successfully allow us to utilize and apply the noncommutativity of phase-space in both quantum mechanics and quantum (cid:28)eld theory. In particular, we brie(cid:29)y explained the Weyl quantization, the Moyal(cid:21)Weyl product, the Bopp-shift transformations, and the Seiberg(cid:21)Witten maps.
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