{"title":"离散维格纳函数素数幂维的几何方法","authors":"A B Klimov, C. Muñoz, J. L. Romero","doi":"10.1088/0305-4470/39/46/016","DOIUrl":null,"url":null,"abstract":"We analyse the Wigner function in prime power dimensions constructed on the basis of the discrete rotation and displacement operators labelled with elements of the underlying finite field. We separately discuss the case of odd and even characteristics and analyse the algebraic origin of the non-uniqueness of the representation of the Wigner function. Explicit expressions for the Wigner kernel are given in both cases.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2006-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1088/0305-4470/39/46/016","citationCount":"46","resultStr":"{\"title\":\"Geometrical approach to the discrete Wigner function in prime power dimensions\",\"authors\":\"A B Klimov, C. Muñoz, J. L. Romero\",\"doi\":\"10.1088/0305-4470/39/46/016\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We analyse the Wigner function in prime power dimensions constructed on the basis of the discrete rotation and displacement operators labelled with elements of the underlying finite field. We separately discuss the case of odd and even characteristics and analyse the algebraic origin of the non-uniqueness of the representation of the Wigner function. Explicit expressions for the Wigner kernel are given in both cases.\",\"PeriodicalId\":87442,\"journal\":{\"name\":\"Journal of physics A: Mathematical and general\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-11-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1088/0305-4470/39/46/016\",\"citationCount\":\"46\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of physics A: Mathematical and general\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1088/0305-4470/39/46/016\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of physics A: Mathematical and general","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1088/0305-4470/39/46/016","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Geometrical approach to the discrete Wigner function in prime power dimensions
We analyse the Wigner function in prime power dimensions constructed on the basis of the discrete rotation and displacement operators labelled with elements of the underlying finite field. We separately discuss the case of odd and even characteristics and analyse the algebraic origin of the non-uniqueness of the representation of the Wigner function. Explicit expressions for the Wigner kernel are given in both cases.
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