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

  title={Explicit Baker–Campbell–Hausdorff–Dynkin formula for spacetime via geometric algebra},
  author={Joseph Clement Wilson and Matt Visser},
  journal={International Journal of Geometric Methods in Modern Physics},
  • J. Wilson, M. Visser
  • Published 1 July 2021
  • Mathematics
  • International Journal of Geometric Methods in Modern Physics
We present a compact Baker–Campbell–Hausdorff–Dynkin formula for the composition of Lorentz transformations [Formula: see text] in the spin representation (a.k.a. Lorentz rotors) in terms of their generators [Formula: see text]: [Formula: see text] This formula is general to geometric algebras (a.k.a. real Clifford algebras) of dimension [Formula: see text], naturally generalizing Rodrigues’ formula for rotations in [Formula: see text]. In particular, it applies to Lorentz rotors within the… 
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