2012/05/20 by D. H. Delphenich, Delphenich, D. H.
Engineering · Mathematics · #Algebraic and Geometric Analysis #Control and Stability of Dynamical Systems #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.1205.4440
openalex publication_date 2012/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is shown that the groups of Euclidian rotations, rigid motions, proper, orthochronous Lorentz transformations, and the complex rigid motions can be represented by the groups of unit-norm elements in the algebras of real, dual, complex, and complex dual quaternions, respectively. It is shown how someof the physically-useful tensors and spinors can be represented by the various kinds of quaternions. The basic notions of kinematical states are described in each case, except complex dual quaternions, where their possible role in describing the symmetries of the Maxwell equations is discussed.