Plane wave solution to Dirac equation

[Josh1079]

Hi, I'm recently reading an introductory text about particle physics and there is a section about the Dirac equation. I think I can understand the solutions for rest particles, but the plane wave solutions appear to be a bit weird to me. For instance, when the upper states are (1 0), the lower states are non zero. Does this mean that when the electron is moving, there is some component of it being a positron?

Thanks!

 

[vanhees71]

It depends on which representation of the Dirac matrices you are using, which components belong to particles and which to antiparticles. Usually you use the Wigner basis, i.e., you take the spin eigenstates for the particle with $\vec{p}=0$ (I discuss the massive case) and then Lorentzboost it rotation free to the frame, where $\vec{p} \neq 0$. Then you get for sure a particle/antiparticle state if you $\vec{p}=0$ solution is accordingly a particle/antiparticle state.

 

[Josh1079]

Um... I think I get it.

Thanks!