Spinor Transformations of Maxwell's Equations

Whilst the greatest effort has been made to ensure the quality of this text, due to the historical nature of this content, in some rare cases there may be minor issues with legibility. Elements of Matrix S for a Proper Lorentz Transformation[1] [2] Previous authors, e.g. Who have given Maxwell's equations in terms of a spinor notation have not concerned themselves with the relativistic invariance of these equations. In the present paper we extend the work of the previous authors, in particular the work of Moliere, in such a way that the equa tions are relativistically invariant in spinor notation. It will turn out that one obtains the same transformation rules for field strengths as one obtains from the more conventional form of relativistic electrodynamics. However, the transforma tions will be somewhat simpler in form and will constitute an orthogonal representation of the proper Lorentz group. The transformations are summarized in section h. The remainder of the paper deals with the proof of the group properties.