## THE DIRAC EQUATION AS THE CONSEQUENCE OF THE QUANTUM-MECHANICAL SPIN 1/2 DOUBLET MODEL

## THE DIRAC EQUATION AS THE CONSEQUENCE OF THE QUANTUM-MECHANICAL SPIN 1/2 DOUBLET MODEL

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*Ivan Krivsky Volodimir Simulik Irina Lamer Zajac Taras *

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## Abstract

The detailed consideration of the relativistic canonical quantum-mechanical model of an arbitrary -�s -multiplet is given. The group-theoretical analysis of the algebra of experimentally observable physical quantities for the s = 1 2 doublet is presented. It is shown that both the Foldy-Wouthuysen equation for the fermionic spin s = 1 2 doublet and the Dirac equation in its local representation are the consequences of the relativistic canonical quantum mechanics of the corresponding doublet. The mathematically welldefined consideration on the level of modern axiomatic approaches to the field theory is provided.

## Keywords

Canonical quantum-mechanics, Schr�odinger-Foldy equation, Dirac equation, Foldy-Wouthuysen representation, spinor field.