Bosonic symmetries of the Dirac equation

We have found on the basis of the symmetry analysis of the standard Dirac equation with nonzero mass the new physically meaningful features of this equation. The new bosonic symmetries of the Dirac equation in both the Foldy–Wouthuysen and the Pauli–Dirac representations are found, among which (together with the 32-dimensional pure matrix algebra of invariance) the new spin s = ( 1 , 0 ) multiplet Poincaré symmetry is proved. In order to carry out the corresponding proofs a 64-dimensional extended real Clifford–Dirac algebra is put into consideration. ► The 64-dimensional extended real Clifford–Dirac algebra is put into consideration. ► Maximal pure matrix algebra of invariance of the Foldy–Wouthuysen equation is found. ► The spin ( 1 , 0 ) Lorentz and Poincaré symmetries of the Dirac equation are proved.