β Scribed by C Codirla; H Osborn
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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 group O(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.
1997 Academic Press
The invariance of Maxwell's equations under Lorentz transformations is the cornerstone of the theory of relativity as expounded in the epoch making paper of Einstein in 1905. In 1909 Cunningham [1] and Bateman showed that Maxwell's equations were also invariant under the larger conformal group. This invariance does not extend to theories containing any mass scale and is violated in quantum field theories, even when true classically, except under very special circumstances so this symmetry has not played a significant role in mainstream theoretical physics. Nevertheless a particular feature of the conformal group is that it extends the usual Lorentz group in allowing transformations to frames undergoing constant acceleration. In the next section show how the conformal group can be used to obtain expressions for the electric and magnetic fields, known also since 1909, corresponding to a charged particle which undergoes constant acceleration or hyperbolic motion. The fields obtained by conformal transformation are nonzero everywhere for all time and are, of course, solutions of Maxwell's equations. They are related to, but not identical with, the standard retarded, or advanced, solutions, since these are zero on half of space-time. We also describe briefly the derivation of these retarded, advanced solutions together with the additional terms which are article no. PH975708 91 0003-4916Γ97 25.00
π SIMILAR VOLUMES
A general account of the interaction of charges with electromagnetic radiation is presented; the charges are treated in the nonrelativistic approximation for Ε½ . simplicity not an essential assumption . The two main approaches in the literature based Ε½ . on either the potentials of the electromagnet