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Explicit closed-form parametrization of SU(3) and SU(4) in terms of complex quaternions and elementary functions

Andre Gsponer
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Abstract

Remarkably simple closed-form expressions for the elements of the groups SU(n), SL(n,R), and SL(n,C) with n=2, 3, and 4 are obtained using linear functions of biquaternions instead of n x n matrices. These representations do not directly generalize to SU(n>4). However, the quaternion methods used are sufficiently general to find applications in quantum chromodynamics and other problems which necessitate complicated 3 x 3 or 4 x 4 matrix calculations.

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Andre Gsponer. 2002-11-22. Explicit closed-form parametrization of SU(3) and SU(4) in terms of complex quaternions and elementary functions. https://arxiv.org/abs/math-ph/0211056

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