Calculation of Spin Group Elements Revisited
Mathematical Physics
2025-04-29 v1 math.MP
Abstract
In this paper, we present a method for calculation of spin groups elements for known pseudo-orthogonal group elements with respect to the corresponding two-sheeted coverings. We present our results using the Clifford algebra formalism in the case of arbitrary dimension and signature, and then explicitly using matrices, quaternions, and split-quaternions in the cases of all possible signatures (p,q) of space up to dimension n=p+q=3. The different formalisms are convenient for different possible applications in physics, engeneering, and computer science.
Cite
@article{arxiv.2412.02772,
title = {Calculation of Spin Group Elements Revisited},
author = {D. S. Shirokov},
journal= {arXiv preprint arXiv:2412.02772},
year = {2025}
}