Retrieving the missed particle-antiparticle degrees of freedom of Dirac particles

The missed particle-antiparticle degrees of freedom are retrieved and the corresponding particle-antiparticle intrinsic space are introduced to study the dynamical symmetry of the Dirac particle. As a result, the particle-antiparticle quantum number appears naturally and the Dirac particle has five quantum numbers instead of four. An anti-symmetry (different from the conventional symmetry) of the Dirac Hamiltonian and a dual symmetry of its eigenfunctions are explored. The $\hat{\kappa}$ operator of the Dirac equation in central potentials is found to be the analog of the helicity operator of the free particle--the alignment of the spin along the angular momentum.