Condensed Matter Physics, 2010, vol. 13, No. 4, p. 43101:115
DOI:10.5488/CMP.13.43101
Title:
FermiBose duality of the Dirac equation and extended real CliffordDirac algebra
Author(s):

I.Yu. Krivsky
(Institute of Electron Physics, National Academy of Sciences of Ukraine, 21 Universitetska Str., 88000 Uzhgorod, Ukraine)
,


V.M. Simulik
(Institute of Electron Physics, National Academy of Sciences of Ukraine, 21 Universitetska Str., 88000 Uzhgorod, Ukraine)

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 FoldyWouthuysen and the PauliDirac representations are found. Among these symmetries (together with the 32dimensional 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 64dimensional extended real CliffordDirac algebra is put into consideration.
Key words:
spinor field, symmetry, grouptheoretical analysis, supersymmetry, FoldyWouthuysen representation, CliffordDirac algebra
PACS:
11.30z., 11.30.Cp., 11.30.j
