English

Spinors in Spacetime Algebra and Euclidean 4-Space

General Mathematics 2017-03-06 v1

Abstract

This article explores the geometric algebra of Minkowski spacetime, and its relationship to the geometric algebra of Euclidean 4-space. Both of these geometric algebras are algebraically isomorphic to the 2x2 matrix algebra over Hamilton's famous quaternions, and provide a rich geometric framework for various important topics in mathematics and physics, including stereographic projection and spinors, and both spherical and hyperbolic geometry. In addition, by identifying the time-like Minkowski unit vector with the extra dimension of Euclidean 4-space, David Hestenes' Space-Time Algebra of Minkowski spacetime is unified with William Baylis' Algebra of Physical Space.

Keywords

Cite

@article{arxiv.1703.01244,
  title  = {Spinors in Spacetime Algebra and Euclidean 4-Space},
  author = {Garret Sobczyk},
  journal= {arXiv preprint arXiv:1703.01244},
  year   = {2017}
}

Comments

16 pages, 3 figures

R2 v1 2026-06-22T18:34:59.302Z