Abstract
As a consequence of invariance under the special conformal transformation, a new conserved four-vector is derived for two massive charged point particles interacting through classical relativistic action-at-a-distance scalar and vector potentials. This represents a generalization of the conservation law discovered for sourceless electromagnetic fields by Bessel-Hagen in 1921. The conserved four-vector is explicitly evaluated for Schild's solution of the equation of motion, corresponding to uniform circular motion. All 15 of the conserved quantities related to the 15-parameter conformal group are now known for Schild's solution which has been extended to cover scalar as well as vector potentials.
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