The Schrodinger-Foldy relativistic canonical quantum mechanics and the derivation of the Dirac equation

TL;DR

This paper develops a relativistic canonical quantum-mechanical model for arbitrary spin multiplets, deriving the Dirac equation and analyzing the algebra of observables, with implications for understanding fermionic particles and antiparticles.

Contribution

It provides a group-theoretical derivation of the Dirac equation from relativistic quantum mechanics and discusses the algebra of observables for spin-1/2 doublets.

Findings

Derivation of Dirac equation from relativistic quantum mechanics.

Analysis of the algebra of physical observables for spin 1/2 doublets.

Discussion on the hypothesis of antiparticle negative mass.

Abstract

The detailed consideration of the relativistic canonical quantum-mechanical model of an arbitrary spin-multiplet is given. The group-theoretical analysis of the algebra of experimentally observables physical quantities for the spin 1/2 doublet is presented. It is shown that both the Foldy-Wouthuysen equation for the fermionic spin 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 well-defined consideration on the level of modern axiomatic approaches to the field theory is provided. The hypothesis of the antiparticle negative mass is discussed briefly in the section conclusions.