Appendix C: Quaternions and special relativity - Dutra, Sergio M. (Cavity Quantum Electrodynamics: The Strange Theory of Light in a Box, 2004)
Complex numbers unify algebra and two dimensional geometry representing rotations on the plane as multiplication by a complex number. This appendix introduces quaternions as an extension of this unification to four dimensions. The quaternion gradient is defined, the quaternion analogues of the Cauchy‐Riemann equations is obtained, and basic quaternion integral theorems are derived. A pedagogic derivation of the quaternion representation of three‐dimensional rotations widely applied in robotics and computer graphics is presented. The appendix closes with a detailed discussion on the application of biquaternions in relativity.