Fermi-Bose duality of the Dirac equation and extended real Clifford-Dirac algebra

Abstract

We have proved on the basis of the symmetry analysis of the standard Dirac equation with nonzero mass that this equation may describe not only fermions of spin 1/2 but also bosons of spin 1. The new bosonic symmetries of the Dirac equation in both the Foldy-Wouthuysen and the Pauli-Dirac representations are found. Among these symmetries (together with the 32-dimensional pure matrix algebra of invariance) the new, physically meaningful, spin 1 Poincare symmetry of equation under consideration is proved. In order to provide the corresponding proofs, a 64-dimensional extended real Clifford-Dirac algebra is put into consideration.

Keywords

• spinor field
• symmetry
• group-theoretical analysis
• supersymmetry
• Foldy-Wouthuysen representation
• Clifford-Dirac algebra