Consequent Quantum Mechanics by Applying 8-Dimensional Spinors in the Dirac Equation

Abstract

Aims: A consequent quantum mechanics was developed by rendering operators also for the charge and rest mass. In this formalism the Dirac equation was extended by applying 8-dimensional spinors for the decomposition of square root in the covariant equation of special relativity. Results: The charge and mass operators defined by 8–dimensional spinors commute with the Hamiltonian of electron and positron in electromagnetic field, but they do not commute for neutrino and quarks. Conclusions: For neutrino the expectation values of the rest mass and charge are zero allowing these particles moving with the speed of light. The momentum of neutrino commutes with the Hamiltonian thus it has a well-defined value for the three types of neutrinos explaining why the neutrinos can oscillate. For quarks neither the rest mass nor the charge operators commute with the Hamiltonian, thus the fractional charge and renormalized mass can be considered as expectation values in the hadron states. Since any charge measurements should give eigenvalues of its operator, no fractional charge can be detected excluding possibility of observing free quarks.