Mathematical Structures of Different Categories of Quantum Fields

Quantum field theory is a covering quantum theory that applies to high-energy processes where particles are created and destroyed. Properties of a quantum field that represents an elementary particle and a quantum field that mediates interaction between particles are analyzed. This analysis relies on fundamental physical principles. The mathematical structure of these fields proves that they are completely different physical objects. A further analysis proves that a quantum field that represents an elementary massive particle and a quantum field that represents a massless particle have a completely different mathematical structure. The results are used in an examination of free spin-1/2 elementary massive particles and other free elementary particles that have an integral spin. Inherent inconsistencies are found for elementary massive particles that have an integral spin and for the Majorana neutrino. The analysis also proves that interaction mediating fields do not represent a genuine particle. In particular, the electroweak theory of the W \(\pm\) and the Z particles has no coherent basis.