Appendix C: Quaternions and special relativity

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 Cauch...

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Veröffentlicht in:Cavity Quantum Electrodynamics: The Strange Theory of Light in a Box S. 293 - 310
1. Verfasser: Dutra, Sergio M.
Format: Buchkapitel
Sprache:Englisch
Veröffentlicht: Hoboken, NJ, USA John Wiley & Sons, Inc 03.12.2004
Schlagworte:
biquaternions
Cayles formula
Lorentz transformations
quaternion gradient
quaternion integral theorems
quaternions
Tetractys
three‐dimensional rotations
ISBN:9780471443384, 0471443387
Online-Zugang:Volltext
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Beschreibung
Zusammenfassung: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.
ISBN:9780471443384
0471443387
DOI:10.1002/0471713465.app3