2017/03/02 by Garret Sobczyk, Sobczyk, Garret
Mathematics · Physics and Astronomy · #15A66 #81P16 #Advanced Mathematical Theories and Applications #Algebraic and Geometric Analysis #FOS: Mathematics #General Mathematics (math.GM) #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.1703.01244
openalex publication_date 2017/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.