E.M.S. Hitzer
Relativistic Physics as Application of Geometric Algebra
K. Adhav (ed.), Proceedings of the International Conference on Relativity 2005 (ICR2005), University of Amravati, India, January 2005, pp. 71-90.
Published at Department of Mathematics, Amravati University, Amravati 444602, India.

Abstract: This review of relativistic physics integrates the works of Hamilton, Grassmann, Maxwell, Clifford, Einstein, Hestenes and lately the Cambridge (UK) Geometric Algebra Research Group. We start with the geometric algebra of spacetime (STA). We show how frames and trajectories are described and how Lorentz transformations acquire their fundamental rotor form. Spacetime dynamics deals with spacetime rotors, which have invariant and frame dependent splits. Spacetime rotor equations yield the proper acceleration (bivector) and the Fermi (vector) derivative.

A first application is given with the relativistic STA formulation of the Lorentz force law, leading to the description of spin precession in magnetic fields and Thomas precession. Now the stage is ready for introducing the STA Maxwell equation, which combines all 4 equations in one single STA equation. STA has procedures to extract from the electromagnetic field strength bivector F, electric and magnetic fields (also for relative motion observers) and field invariants, field momentum and stress-energy tensor. The Leonhard-Wiechert potential gives the retarded field of a point charge.

In addition we formulate the Dirac equation in STA, both massless and massive. From the Dirac equation we can derive STA expressions for Dirac observables. Plane wave states are described with the help of rotor decomposition. Finally we briefly review a STA gauge theory of gravity built on displacement and rotation gauge principles.


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