Classical Fields in Special Relativity

Classical field equations are ordinarily postulated, imposed on a background space-time. Here it is shown that in relativity such fields can be a natural consequence of the underlying space-time structure; they need not and can not be arbitrarily defined. Indeed, under general assumptions, a classical field that results in a four-acceleration on flat space-time must satisfy Maxwell's equations. The field can also be a solution of a Proca equation, if it is assumed, in addition, to be derived from a vector potential with zero divergence. Some analogous result may be possible for quantum fields, given the proper underlying spacetime structure.