Conserved quantities associated with conformal invariance for the Wheeler-Feynman two-body vector interaction

A. unified derivation is presented for obtaining the fifteen conserved quantities, associated with conformal invariance, for the Wheeler-Feynman two-body action-at-a-distance vector interaction. Although it is well known that the inhomogeneous Lorentz group of transformations leads to the conserved energy-momentum vector and to the conserved angular momentum-lorentz momentum tensor, it has not previously been shown that the dilation transformation (without scaling of the mass) leads to the conserved dilation scalar and that the acceleration transformation leads to the conserved conformal vector, which was originally obtained without explicit use of the acceleration transformation. A. master equation is derived from the equations of motion, which are obtained from the Wheeler-Feynman action. This master equation is a generalization, applicable to any spacetime transformation, of the one previously presented in the literature that is applicable only to the inhomogeneous Lorentz group of transformations. Substitution of each infinitesimal conformal transformation into this master equation yields the corresponding conserved quantity.