Оn the group-theoretical foundations for Fermi – Bose duality of the spinor field. Solutions and conservation laws

Abstract

The property of Fermi – Bose duality of the Dirac equation with nonzero mass is proved on the basis of generalized Clifford – Dirac algebra and group-theoretical analysis of the spinor field. The Foldy – Wouthuysen representation is used as a starting ground for consideration and the results for standard Dirac formalism are proved to be the simple consequences of such consideration. It is shown that the Dirac equation can describe not only fermionic but also the bosonic states. The proof of our assertion is given on the example of the existence of bosonic symmetries and solutions of the Dirac equation. Furthermore, the bosonic conservation laws are proved to be the consequences of the Dirac equation. Key words: the spinor field, the Dirac equation, the Foldy – Wouthuysen representation, fermions, bosons.