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

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.

arXiv commentSubmitted to Journal of Mathematical Physics, 17 pages, 1 tables

References in corpus (1)

• Baker-Campbell-Hausdorff relation for special unitary groups SU(N)

Cited by in corpus (5)

• An Introduction to Cartan's KAK Decomposition for QC Programmers
• Quaternions in mathematical physics (1): Alphabetical bibliography
• The physical heritage of Sir W.R. Hamilton
• On Parametrization of the Linear GL(4,C) and Unitary SU(4) Groups in Terms of Dirac Matrices
• 4 x 4 matrices in Dirac parametrization: inversion problem and determinant