The Standard Model of Elementary Particles is based on elementary excitations classified by a single spin variable (non-negative half-integer) attributed to the irreducible representations of the rotation group in three dimensions. This feature originates from a theorem of Wigner [1,2], the derivation of which utilizes a homology between the symmetry group SL(2,C) and the Lorentz group, the homogeneous symmetry of Minkowski space. In recent work [3] it has been shown that the representations of SL(2,C) and the Lorentz group differ fundamentally, and that Wigner’s theorem does not apply to the latter. Consequently, elementary fields have to be classified by two indices (j, k), each a non-negative half-integer. Correspondingly, there is also no need to introduce so-called internal symmetries, because the corresponding degrees of freedom follow directly from the second index. Furthermore, owing to the the product-nature of the representations, a mechanism can be suggested that interprets interaction as simple propagation between field factors of identical sub-index j or k [4]. This would remove the embarrassingly high number of free interaction parameters in the Standard Model.