Abstract
The problem of determining the representation matrices of SU(4) is investigated. A convenient set of parameters is first introduced by writing the general element of the group as a product of exponential functions of the generators, and the generators are expressed as differential operators involving these parameters. Special matrix elements of finite transformations with a SU(3) singlet as the initial state are then obtained by solving the eigenvalue equation of the quadratic Casimir operator of SU(4). The solution has the form of a product of elementary functions and threed jm′m functions of SU(2) and is free from summation over intermediate states. By expanding one of thed jm′m functions in an appropriate series a sum rule for the special matrix elements of the permutation operator 1234→3412 is obtained. The discussions are strictly confined to SU(4), but, some of the results given here can be extended to unitary groups of higher dimensions.
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Basu, B.K., Majumdar, S.D. Finite transformations of SU(4). Czech J Phys 23, 1149–1158 (1973). https://doi.org/10.1007/BF01591196
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DOI: https://doi.org/10.1007/BF01591196