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

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

Volodimir Simulik    Ivan Krivsky    Irina Lamer    

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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 field, fermions, bosons, Clifford algebra, new supersymmetry.