The Comparison between the Infinitesimal Operators for SU(3) and Boson Operators in Cartan-Weyl Basis

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We present the detailed calculation of the infinitesimal operators and the boson operators for SU (3) in Cartan-Weyl basis. They have been used extensively as theoretical models for particle physics. We make a comparison between them, alongside with SL(3,c), which displays the concise appearance.
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