Clifford Algebra Derivation of the Characteristic Hypersurfaces of Maxwell's Equations

Details Clifford Algebra Derivation of the Characteristic Hypersurfaces of Maxwell's Equations Clifford Algebra Derivation of the Characteristic Hypersurfaces of Maxwell's Equations

1992-11-14

arxiv.org/abs/hep-th/9211062v1

Physics

High Energy Physics

High Energy Physics - Theory

6 pages

Scientific paper

An alternative, pedagogically simpler derivation of the allowed physical wave fronts of a propagating electromagnetic signal is presented using geometric algebra. Maxwell's equations can be expressed in a single multivector equation using 3D Clifford algebra (isomorphic to Pauli algebra spinorial formulation of electromagnetism). Subsequently one can more easily solve for the time evolution of both the electric and magnetic field simultaneously in terms of the fields evaluated only on a 3D hypersurface. The form of the special "characteristic" surfaces for which the time derivative of the fields can be singular are quickly deduced with little effort.

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