Advantages of the Mathematical Structure of a Dirac Fermion

The mathematical structure of quantum field theories of first order and of second order partial differential equations is analyzed. Relativistic properties of the Lagrangian density and the dimension of its elements are examined. The analysis is restricted to elementary massive particles that are elements of the Standard Model of particle physics. In the case of the first order Dirac equation, the dimensionless 4-vector γµ and the partial 4-derivative ∂µ whose dimension is [L−1],
are elements of the mathematical structure of the theory. On the other hand, the mathematical structure of second order quantum equations has no dimensionless 4-vector which is analogous to γµ of the linear equation. It is proved that this deficiency is the root of inherent theoretical inconsistencies of second order quantum equations. Problems of the Klein-Gordon particle, the electroweak theory of the W±, Z particles and the Higgs boson theory are discussed.