Two-component first-order equations for the quantum-relativistic electron

It is shown that the free Dirac equation can be split into a pair of independent two-component first-order equations. The solutions lambda and μ of the two-component equations are obtained as linear superpositions of the ordinary solutions psi and psi-bar of the Dirac equation and its adjoint one. The theory allows a simple interpretation in terms of ''particles'' and ''antiparticles'' consisting of electron-positron superposition states. The C, P and T invariance properties of the two-component equations are investigated. The problem is made intricate by the well-known ambiguities in the definitions of C, P and T for Fermi-Dirac particles. It follows that physically equivalent definitions of C, P and T may involve completely different symmetry properties for the two-component equations. The equations are coupled by the electromagnetic interaction. (author)