Derivation of relativistic quantum mechanics

В. М. Симулик, I.Yu. Krivsky

A brief review of the different ways of the Dirac equation derivation is given. The foundations of the relativistic canonical quantum mechanics of a fermionic doublet are formulated. In our approach the Dirac equation is derived from the main equation of relativistic canonical quantum mechanics. In the formalism of relativistic canonical quantum mechanics the absence of necessity to appeal for the conception of the negative mass of the antiparticle is shown.

Mark Goodall

I.Yu. Krivsky, В. М. Симулик, T.M. Zajac +1 more

The derivation of the Dirac and Maxwell equations from the first principles of relativistic canonical quantum mechanics (RCQM) is demonstrated. The formalism of the RCQM is constructed on the basis of a self-consistent system of axioms. The important conclusion, that an arbitrary physical and mathematical information, which contains in the model of RCQM, directly and unambiguously is translated into the corresponding information in the model given by the Dirac equation, is formulated.

Koshun Suto

K. V. Roberts

H. Y. Cui

The derivation becomes possible when we find a new formalism which connects the relativistic mechanics with the quantum mechanics. In this paper, we explore the quantum wave nature from the Newtonian mechanics by using a concept: velocity field. At first, we rewrite the relativistic Newton's second law as a field equation in terms of the velocity field, which directly reveals a new relationship connecting to the quantum mechanics. Next, we show that the Dirac equation can be derived from the field equation in a rigorous and consistent manner.