Consequences of the Dimension of the Quantum Function Ψ

Textbooks on classical physics adequately discuss the dimension concept of physical quantities. Alternatively, it turns out that quantum textbooks generally ignore the dimension of the quantum function Ψ. Furthermore, different quantum field theories implicitly assign different values to this concept. This article discusses the dimension of the quantum function Ψ of several theories. It proves that this concept yields effective criteria for the coherence of quantum field theories. These criteria show that the Dirac electron theory has the required properties. On the other hand, there are unsettled problems with the electroweak theory of the W± particles and with the Klein-Gordon theory of charged particles. The analysis shows a short proof of the inability to construct the required Maxwellian 4-current of the electroweak theory of the W± particles. This outcome indicates the effective properties of the dimension of the quantum function Ψ. The discussion proves several other new constraints on the 4-current of a quantum theory of a charged particle.