Abstract
We are trying to build up a theory in which all the supplementary conditions are considered as constraint equations imposed on the wave function and implying that only 2s+1 (s=spin) of its components are really independent. In the already treated free field case, all the elementary particles obey the Klein-Gordon equation of motion. To introduce the electromagnetic field in a general way we consider a basic interaction involving the transformation matrix of the wave function. A process is described, by means of which a gauge invariant equation of motion can be constructed. The theory is renormalizable and describes particles having the normal gyromagnetic factor 2 for any spin value.
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