Explicit Baker–Campbell–Hausdorff–Dynkin formula for spacetime via geometric algebra

We present a compact Baker–Campbell–Hausdorff–Dynkin formula for the composition of Lorentz transformations [Formula: see text] in spin representation (a.k.a. rotors) terms their generators text]: This is general to geometric algebras real Clifford algebras) dimension text], naturally generalizing Rodrigues’ rotations text]. In particular, it applies rotors within framework Hestenes’ spacetime algebra, and provides an efficient method composing generators. Computer implementations are possible with complex matrix realized by Pauli matrices. The applied relativistic text]-velocities yielding simple expressions resulting boost concomitant Wigner angle.