On the Postulational Basis of the Theory of Elementary Particles

A set of postulates is formulated which leads to the relativistic wave equations of present quantum mechanics. The mathematical difference between the usual non-linear interaction terms and terms which introduce essential non-linearities in the equations is discussed. It is proved that every particle must possess an antiparticle unless at least one of the basic postulates is discarded. The connection between the rest mass of the particle, the minimal equation of the $\alpha$-matrices, and the general commutation relations of the $\alpha$-matrices is derived and discussed. It is proved that for a particle of spin ½ there is only one possible wave equation, while for a particle of spin 1 there are others besides the usual scalar and vector equations. One such example is given.