Abstract
We show that the free Dirac equation can be split into a pair of independent two-component first-order equations. The solutions λ and μ of the two-component equations are obtained as linear superpositions of the ordinary solutions ψ and $$\bar \psi $$ 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. TheC, P andT invariance properties of the two-component equations are investigated. The problem is made intricate by the well-known ambiguities in the definitions ofC, P andT for Fermi-Dirac particles. It follows that physically equivalent definitions ofC, P andT may involve completely different symmetry properties for the two-component equations. The equations are coupled by the electromagnetic interaction.
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