1984/01/01 by Patrick Girard · 1 citation
Mathematics · #Algebraic and Geometric Analysis #Mathematics and Applications #Physics #Quaternion #Group (periodic table) #Theory of relativity #Classical mechanics #Tests of special relativity #Conformal group #Group theory #Kinematics #Lorentz group #Special relativity #Test theories of special relativity #General covariance #Dirac equation #Motion (physics) #Mathematical physics #Lorentz transformation #Clifford algebra #Quaternion algebra #General relativity #Algebra over a field #Conformal symmetry #Four-force #Conformal map #Quantum mechanics #Mathematical analysis #Pure mathematics #Geometry #Mathematics #Subalgebra
paper · doi:10.1088/0143-0807/5/1/007
openalex publication_date 1984/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
The paper shows how various physical covariance groups: SO(3), the Lorentz group, the general theory of relativity group, the Clifford algebra SU(2) and the conformal group can easily be related to the quaternion group. The quaternion calculus is introduced and several physical applications: crystallography the kinematics of rigid body motion, the Thomas precession the special theory of relatively, classical electromagnetism, the equation of motion of the general theory of relativity, and Dirac's relativistic wave equation are discussed.