Abstract
The role of the conformal group in electrodynamics in four space-time dimensions is reexamined. As a pedagogic example we use the application of conformal transformations to find the electromagnetic field for a charged particle moving with a constant relativistic acceleration from the Coulomb electric field for the particle at rest. We also reconsider the reformulation of Maxwell's equations on the projective cone, which is isomorphic to a conformal compactification on Minkowski space, so that conformal transformations, belonging to the groupO(4,2), are realised linearly. The resulting equations are different from those postulated previously and respect additional gauge invariances which play an essential role in ensuring consistency with conventional electrodynamics on Minkowski space. The solution on the projective cone corresponding to a constantly accelerating charged particle is discussed.
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