Lorentz Boosts and Wigner Rotations: Self-Adjoint Complexified Quaternions

In this paper, Lorentz boosts and Wigner rotations are considered from a (complexified) quaternionic point of view. It is demonstrated that, for suitably defined self-adjoint complex 4-velocity, pure can be phrased in terms the quaternion square root relative 4-velocity connecting two inertial frames. Straightforward computations then lead to quite explicit relatively simple algebraic formulae composition 4-velocities angle. The rotation subsequently related generic non-associativity three 4-velocities, necessary sufficient condition developed associativity hold. Finally, authors relate specific implementation Baker–Campbell–Hausdorff theorem. As compared ordinary 4×4 transformations, use complexified quaternions leads, computational view, storage savings more rapid computations, pedagogical view formulae.