量子光学中q-变形模型的忠实矩阵表示
L. Hanna, Abdullah Alazemi, Anwar Al-Dhafeeri
{"title":"量子光学中q-变形模型的忠实矩阵表示","authors":"L. Hanna, Abdullah Alazemi, Anwar Al-Dhafeeri","doi":"10.1155/2022/6737287","DOIUrl":null,"url":null,"abstract":"<jats:p>Consider the <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\n <mi>q</mi>\n </math>\n </jats:inline-formula>-deformed Lie algebra, <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\n <msub>\n <mrow>\n <mi mathvariant=\"fraktur\">t</mi>\n </mrow>\n <mrow>\n <mi>q</mi>\n </mrow>\n </msub>\n <mo>:</mo>\n <msub>\n <mrow>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <msub>\n <mrow>\n <mover accent=\"true\">\n <mi>K</mi>\n <mo>^</mo>\n </mover>\n </mrow>\n <mrow>\n <mn>1</mn>\n </mrow>\n </msub>\n <mo>,</mo>\n <msub>\n <mrow>\n <mover accent=\"true\">\n <mi>K</mi>\n <mo>^</mo>\n </mover>\n </mrow>\n <mrow>\n <mn>2</mn>\n </mrow>\n </msub>\n </mrow>\n </mfenced>\n </mrow>\n <mrow>\n <mi>q</mi>\n </mrow>\n </msub>\n <mo>=</mo>\n <mfenced open=\"(\" close=\")\" separators=\"|\">\n <mrow>\n <mn>1</mn>\n <mo>−</mo>\n <mi>q</mi>\n </mrow>\n </mfenced>\n <msub>\n <mrow>\n <mover accent=\"true\">\n <mi>K</mi>\n <mo>^</mo>\n </mover>\n </mrow>\n <mrow>\n <mn>1</mn>\n </mrow>\n </msub>\n <msub>\n <mrow>\n <mover accent=\"true\">\n <mi>K</mi>\n <mo>^</mo>\n </mover>\n </mrow>\n <mrow>\n <mn>2</mn>\n </mrow>\n </msub>\n <mo>,</mo>\n <msub>\n <mrow>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <msub>\n <mrow>\n <mover accent=\"true\">\n <mi>K</mi>\n <mo>^</mo>\n </mover>\n </mrow>\n <mrow>\n <mn>3</mn>\n </mrow>\n </msub>\n <mo>,</mo>\n <msub>\n <mrow>\n <mover accent=\"true\">\n <mi>K</mi>\n <mo>^</mo>\n </mover>\n </mrow>\n <mrow>\n <mn>1</mn>\n </mrow>\n </msub>\n </mrow>\n </mfenced>\n </mrow>\n <mrow>\n <mi>q</mi>\n </mrow>\n </msub>\n <mo>=</mo>\n <mi>s</mi>\n <msub>\n <mrow>\n <mover accent=\"true\">\n <mi>K</mi>\n <mo>^</mo>\n </mover>\n </mrow>\n <mrow>\n <mn>3</mn>\n </mrow>\n </msub>\n </math>\n </jats:inline-formula>, <jats:inline-formula>\n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\n <msub>\n <mrow>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <msub>\n <mrow>\n <mover accent=\"true\">\n <mi>K</mi>\n <mo>^</mo>\n </mover>\n </mrow>\n <mrow>\n <mn>1</mn>\n </mrow>\n </msub>\n <mo>,</mo>\n <msub>\n <mrow>\n <mover accent=\"true\">\n <mi>K</mi>\n <mo>^</mo>\n </mover>\n </mrow>\n <mrow>\n <mn>4</mn>\n </mrow>\n </msub>\n </mrow>\n </mfenced>\n </mrow>\n <mrow>\n <mi>q</mi>\n </mrow>\n </msub>\n <mo>=</mo>\n <mi>s</mi>\n <msub>\n <mrow>\n <mover accent=\"true\">\n <mi>K</mi>\n <mo>^</mo>\n </mover>\n </mrow>\n <mrow>\n <mn>4</mn>\n </mrow>\n </msub>\n <mo>,</mo>\n <msub>\n <mrow>\n <mfenced open=\"[\" close=\"]\" separators=\"|\">\n <mrow>\n <msub>\n <mrow>\n <mover accent=\"true\">\n <mi>K</mi>\n <mo>^</mo>\n </mover>\n </mrow>\n <mrow>\n <mn>3</mn>\n </mrow>\n </msub>\n <mo>,</mo>\n <msub>\n <mrow>\n <mover accent=\"true\">\n <mi>K</mi>\n <mo>^</mo>\n </mover>\n </mrow>\n <mrow>\n <mn>2</mn>\n </mrow>\n </msub>\n </mrow>\n </mfenced>\n </mrow>\n <mrow>\n <mi>q</mi>\n </mrow>\n </msub>\n <mo>=</mo>\n <mi>t</mi>\n <msub>\n <mrow>\n <mover accent=\"true\">\n <mi>K</mi>\n <mo>^</mo>\n </mover>\n </mrow>\n <mrow>\n <mn>3</mn>\n </mrow>\n </msub>\n <mo>,</mo>\n ","PeriodicalId":301406,"journal":{"name":"Int. J. Math. Math. Sci.","volume":"115 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Faithful Matrix Representations of q-Deformed Models in Quantum Optics\",\"authors\":\"L. Hanna, Abdullah Alazemi, Anwar Al-Dhafeeri\",\"doi\":\"10.1155/2022/6737287\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<jats:p>Consider the <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M1\\\">\\n <mi>q</mi>\\n </math>\\n </jats:inline-formula>-deformed Lie algebra, <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M2\\\">\\n <msub>\\n <mrow>\\n <mi mathvariant=\\\"fraktur\\\">t</mi>\\n </mrow>\\n <mrow>\\n <mi>q</mi>\\n </mrow>\\n </msub>\\n <mo>:</mo>\\n <msub>\\n <mrow>\\n <mfenced open=\\\"[\\\" close=\\\"]\\\" separators=\\\"|\\\">\\n <mrow>\\n <msub>\\n <mrow>\\n <mover accent=\\\"true\\\">\\n <mi>K</mi>\\n <mo>^</mo>\\n </mover>\\n </mrow>\\n <mrow>\\n <mn>1</mn>\\n </mrow>\\n </msub>\\n <mo>,</mo>\\n <msub>\\n <mrow>\\n <mover accent=\\\"true\\\">\\n <mi>K</mi>\\n <mo>^</mo>\\n </mover>\\n </mrow>\\n <mrow>\\n <mn>2</mn>\\n </mrow>\\n </msub>\\n </mrow>\\n </mfenced>\\n </mrow>\\n <mrow>\\n <mi>q</mi>\\n </mrow>\\n </msub>\\n <mo>=</mo>\\n <mfenced open=\\\"(\\\" close=\\\")\\\" separators=\\\"|\\\">\\n <mrow>\\n <mn>1</mn>\\n <mo>−</mo>\\n <mi>q</mi>\\n </mrow>\\n </mfenced>\\n <msub>\\n <mrow>\\n <mover accent=\\\"true\\\">\\n <mi>K</mi>\\n <mo>^</mo>\\n </mover>\\n </mrow>\\n <mrow>\\n <mn>1</mn>\\n </mrow>\\n </msub>\\n <msub>\\n <mrow>\\n <mover accent=\\\"true\\\">\\n <mi>K</mi>\\n <mo>^</mo>\\n </mover>\\n </mrow>\\n <mrow>\\n <mn>2</mn>\\n </mrow>\\n </msub>\\n <mo>,</mo>\\n <msub>\\n <mrow>\\n <mfenced open=\\\"[\\\" close=\\\"]\\\" separators=\\\"|\\\">\\n <mrow>\\n <msub>\\n <mrow>\\n <mover accent=\\\"true\\\">\\n <mi>K</mi>\\n <mo>^</mo>\\n </mover>\\n </mrow>\\n <mrow>\\n <mn>3</mn>\\n </mrow>\\n </msub>\\n <mo>,</mo>\\n <msub>\\n <mrow>\\n <mover accent=\\\"true\\\">\\n <mi>K</mi>\\n <mo>^</mo>\\n </mover>\\n </mrow>\\n <mrow>\\n <mn>1</mn>\\n </mrow>\\n </msub>\\n </mrow>\\n </mfenced>\\n </mrow>\\n <mrow>\\n <mi>q</mi>\\n </mrow>\\n </msub>\\n <mo>=</mo>\\n <mi>s</mi>\\n <msub>\\n <mrow>\\n <mover accent=\\\"true\\\">\\n <mi>K</mi>\\n <mo>^</mo>\\n </mover>\\n </mrow>\\n <mrow>\\n <mn>3</mn>\\n </mrow>\\n </msub>\\n </math>\\n </jats:inline-formula>, <jats:inline-formula>\\n <math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" id=\\\"M3\\\">\\n <msub>\\n <mrow>\\n <mfenced open=\\\"[\\\" close=\\\"]\\\" separators=\\\"|\\\">\\n <mrow>\\n <msub>\\n <mrow>\\n <mover accent=\\\"true\\\">\\n <mi>K</mi>\\n <mo>^</mo>\\n </mover>\\n </mrow>\\n <mrow>\\n <mn>1</mn>\\n </mrow>\\n </msub>\\n <mo>,</mo>\\n <msub>\\n <mrow>\\n <mover accent=\\\"true\\\">\\n <mi>K</mi>\\n <mo>^</mo>\\n </mover>\\n </mrow>\\n <mrow>\\n <mn>4</mn>\\n </mrow>\\n </msub>\\n </mrow>\\n </mfenced>\\n </mrow>\\n <mrow>\\n <mi>q</mi>\\n </mrow>\\n </msub>\\n <mo>=</mo>\\n <mi>s</mi>\\n <msub>\\n <mrow>\\n <mover accent=\\\"true\\\">\\n <mi>K</mi>\\n <mo>^</mo>\\n </mover>\\n </mrow>\\n <mrow>\\n <mn>4</mn>\\n </mrow>\\n </msub>\\n <mo>,</mo>\\n <msub>\\n <mrow>\\n <mfenced open=\\\"[\\\" close=\\\"]\\\" separators=\\\"|\\\">\\n <mrow>\\n <msub>\\n <mrow>\\n <mover accent=\\\"true\\\">\\n <mi>K</mi>\\n <mo>^</mo>\\n </mover>\\n </mrow>\\n <mrow>\\n <mn>3</mn>\\n </mrow>\\n </msub>\\n <mo>,</mo>\\n <msub>\\n <mrow>\\n <mover accent=\\\"true\\\">\\n <mi>K</mi>\\n <mo>^</mo>\\n </mover>\\n </mrow>\\n <mrow>\\n <mn>2</mn>\\n </mrow>\\n </msub>\\n </mrow>\\n </mfenced>\\n </mrow>\\n <mrow>\\n <mi>q</mi>\\n </mrow>\\n </msub>\\n <mo>=</mo>\\n <mi>t</mi>\\n <msub>\\n <mrow>\\n <mover accent=\\\"true\\\">\\n <mi>K</mi>\\n <mo>^</mo>\\n </mover>\\n </mrow>\\n <mrow>\\n <mn>3</mn>\\n </mrow>\\n </msub>\\n <mo>,</mo>\\n \",\"PeriodicalId\":301406,\"journal\":{\"name\":\"Int. 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引用次数: 0
摘要
考虑q变形李代数，t q:K ^ 1,K ^ 2q = 1−q K^ 1k ^ 2,K ^ 3,K ^ 1q = s K ^ 3,K ^1, k ^本文章由计算机程序翻译，如有差异，请以英文原文为准。
On Faithful Matrix Representations of q-Deformed Models in Quantum Optics
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