APPLICATION OF THE GENERALIZED CLIFFORD-DIRAC ALGEBRA TO THE PROOF OF THE DIRAC EQUATION FERMI-BOSE DUALITY

Year 2013, Volume: 3 Issue: 1, 46 - 61, 01.06.2013

Volodimir Simulik Ivan Krivsky Irina Lamer

Abstract

The consideration of the bosonic properties of the Dirac equation with arbitrary mass has been continued. As the necessary mathematical tool the structure and different representations of the 29-dimensional extended real Clifford-Dirac algebra Phys. Lett. A., 2011, v.375, p.2479 are considered briefly. As a next step we use the start from the Foldy-Wouthuysen representation. On the basis of these two ideas the property of Fermi-Bose duality of the Dirac equation with nonzero mass is proved. The proof is given on the three maim examples: bosonic symmetries, bosonic solutions and bosonic conservation laws. It means that Dirac equation can describe not only the fermionic but also the bosonic states.

Keywords

Dirac equation, Foldy-Wouthuysen representation, spinor Şeld, fermions, bosons, Clifford algebra, new supersymmetry

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