Quantizing relativistic action-at-a-distance mechanics



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A wave equation for charged particles whose non-quantal dynamics is regulated by a relativistic action-at-a-distance formulation of dynamics is presented. Resolutions are given for what has heretofore been the two principle obstacles to construction of such an equation. One, a quantization procedure is developed on the epistemological foundation afforded by regarding the wave aspect of deBroglie's second solution as a manifestation of a classical electromagnetic background with a Lorentz invariant energy spectral density. Such a procedure does not give time a special status and is therefore applicable directly to any formulation of dynamics. Two, a single parameter Lagrangian is proposed which leads to equations of motion free of certain difficulties endemic to the Fokker formulation of relativistic action-at-a-distance dynamics. Finally, comments are made regarding the possible physical and philosophical impact of these resolutions and the resulting wave equation.