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

2002/11/22 by André Gsponer, Andre Gsponer, Gsponer, Andre · 2 citations
Chemistry · Computer Science · Mathematics · Physics and Astronomy · #Advanced NMR Techniques and Applications #Matrix Theory and Algorithms #Numerical methods for differential equations #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/0211056

Submitted to Journal of Mathematical Physics, 17 pages, 1 tables

arxiv created 2002/11/22 · arxiv updated 2009/11/30

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.

Citations

• Lie Groups, Lie Algebras, and Some of Their Applications

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• 4 x 4 matrices in Dirac parametrization: inversion problem and determinant

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