量子光学中q-变形模型的忠实矩阵表示

Int. J. Math. Math. Sci. Pub Date : 2022-09-19 DOI:10.1155/2022/6737287
L. Hanna, Abdullah Alazemi, Anwar Al-Dhafeeri
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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 ^
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On Faithful Matrix Representations of q-Deformed Models in Quantum Optics
Consider the q -deformed Lie algebra, t q : K ^ 1 , K ^ 2 q = 1 − q K ^ 1 K ^ 2 , K ^ 3 , K ^ 1 q = s K ^ 3 , K ^ 1 , K ^ 4 q = s K ^ 4 , K ^ 3 , K ^ 2 q = t K ^ 3 ,
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Int. J. Math. Math. Sci.
Int. J. Math. Math. Sci.
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