The foundations of the mathematical structure of quantum theories of a massive particle are the basis of this analysis. It proves the coherence of the particle-wave duality of quantum theories and the principle of complementarity as well. Furthermore, the noncommutativity of Hermitian operators proves that quantum theories are inherently indeterministic. This feature does not deny the fact that the classical limit of quantum theories agrees with classical physics. It is also shown that the foundations of the mathematical structure of quantum theories impose constraints on any specific quantum theory. It is proved that the first-order Dirac theory is consistent with all constraints. In contrast, second-order theories, such as the Klein-Gordon, the electroweak theory of the W± and the Z particles, and the Higgs boson theory fail to do that. An analogous analysis proves that also the Majorana neutrino theory is inconsistent with fundamental requirements. Similarly, inconsistencies of Proca’s idea about a massive photon are shown.