Multiplication rule of similarity transformations in the coherent state representation and its mapping onto quantum optical generalized ABCD law |
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| Authors: | Shu-guang Liu Hong-yi Fan |
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| Affiliation: | a Department of Applied Mathematics and Physics, Anhui University of Technology and Science, Wuhu, Anhui 241000, China
b Department of Material Science and Engineering, University of Science and Technology of China, Hefei, Anhui 230026, China |
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| Abstract: | We find that classical similarity transformations in the coherent state representation projects onto the similarity transformation operators (STO), these operators constitute a loyal representation of symplectic group. Remarkably, the multiplication rule of the STOs naturally leads to the quantum optical generalized ABCD law, which is the quantum mechanical correspondence of the classical optical ABCD law. Throughout the whole derivation, the technique of integration within an ordered product (IWOP) of operators is employed. |
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| Keywords: | Generalized ABCD law Matrix optics Similarity transformation IWOP technique |
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