In the system of units where h=c=1, the dimension of a physical object can be written in the form [Ln], where L denotes length. The innovative features of this work depend on the analysis of the dimension of the quantum function ψ. This analysis yields new arguments concerning the coherence of quantum theories. The dimension of the Dirac and the Schroedinger functions ψ is [L-3/2]. This fractional dimension enables the construction of crucial theoretical expressions for the Hilbert space and the expectation value of physical operators. On the other hand, the analysis proves that problems exist with quantum fields of elementary massive particles whose function o has the [L-1] dimension, such as the Klein-Gordon theory, the electroweak theory of the W±, Z particles, and the Higgs boson theory.
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