Explicit closed-form parametrization of SU(3) and SU(4) in terms of complex quaternions and elementary functions
Mathematical Physics
2007-05-23 v2 math.MP
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.
Keywords
Cite
@article{arxiv.math-ph/0211056,
title = {Explicit closed-form parametrization of SU(3) and SU(4) in terms of complex quaternions and elementary functions},
author = {Andre Gsponer},
journal= {arXiv preprint arXiv:math-ph/0211056},
year = {2007}
}
Comments
Submitted to Journal of Mathematical Physics, 17 pages, 1 tables