English

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.

Keywords

Cite

@article{arxiv.2412.02772,
  title  = {Calculation of Spin Group Elements Revisited},
  author = {D. S. Shirokov},
  journal= {arXiv preprint arXiv:2412.02772},
  year   = {2025}
}
R2 v1 2026-06-28T20:21:59.407Z