Particle-antiparticle degrees of freedom and related quantum number for dirac particles

The particle-antiparticle degrees of freedom and the corresponding 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 of the Dirac Hamiltonian and a dual symmetry of its eigen functions are explored. The κ-circumflex 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. (authors)