Unsettled Problems of Second-Order Quantum Theories of Elementary Particles

The physical community agrees that the variational principle is a cornerstone of a quantum fieldstheory (QFT) of an elementary particle. This approach examines the variation of the action of aLagrangian density whose form isS=∫d4xL(ψ,ψ;�).The dimension of the actionSandd4xprove that the quantum functionψof any specific Lagrangian densityL(ψ,ψ;�)has a definitedimension. This evidence determines the results of new consistency tests of QFTs. This workapplies these tests to several kinds of quantum functions of a QFT of elementary particles. Itproves that coherent results are derived from the standard form of quantum electrodynamics whichdepends on the Dirac linear equation of a massive charged particle and Maxwell theory of theelectromagnetic fields. In contrast, contradictions stem from second-order quantum theories of anelementary particle, such as the Klein-Gordon equation and the electroweak theory of theW�boson. An observation of the literature that discusses the latter theories indicates that they do notsettle the above-mentioned crucial problems. This issue supports the main results of this work.