Physical Science International Journal <p style="text-align: justify;"><strong>Physical Science International Journal (ISSN:&nbsp;2348-0130) </strong>publishes original research articles, review articles and short communications, in all areas of Physics, Chemistry and Earth Sciences. This is a quality controlled, peer-reviewed, open access INTERNATIONAL journal.</p> Physical Science International Journal en-US Physical Science International Journal 2348-0130 Unsettled Problems of Second-Order Quantum Theories of Elementary Particles <p>The physical community agrees that the variational principle is a cornerstone of a quantum fields theory (QFT) of an elementary particle. This approach examines the variation of the action of&nbsp;a Lagrangian density whose form is \(S = \int d^4 x \mathcal {L}(\psi,\psi_{,\mu}).\) The dimension of the action \(S\) and \(d^4x\) prove that the quantum function \(\psi\) of any specific Lagrangian density \(\mathcal {L}(\psi,\psi_{,\mu})\) has a definite dimension. This evidence determines the results of new consistency tests of QFTs. This work applies these tests to several kinds of quantum functions of a QFT of elementary particles. It proves that coherent results are derived from the standard form of quantum electrodynamics which depends on the Dirac linear equation of a massive&nbsp;charged particle and Maxwell theory of the electromagnetic fields. In contrast, contradictions stem from second-order quantum theories of an elementary particle, such as the Klein-Gordon equation and the electroweak theory of the \(W^\pm\) boson. An observation of the literature that discusses the latter theories indicates that they do not settle the above-mentioned crucial problems. This issue supports the main results of this work.</p> E. Comay ##submission.copyrightStatement## 2021-10-25 2021-10-25 1 10 10.9734/psij/2021/v25i730267