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## Main Question or Discussion Point

So it is said that a basis for the plane wave solutions to the Dirac equation are of the form (p denotes the four-momentum vector) [itex]e^{-i p \cdot x} u^{(s)}[/itex] (for particles) and [itex]e^{i p \cdot x} v^{(s)}[/itex] (for antiparticles), with s = 1 or 2 (and u and v having predetermined structure).

I'm reading in Griffiths' Introduction to Elementary Particles and there he derives the above, and in doing so he says (p233, on top) that e.g. the solution [itex]e^{-i p \cdot x} v^{(s)}[/itex] isn't allowed since it blows up as the three-space momentum [itex]\mathbf p \to 0[/itex]. However, why is this a sufficient reason to simply neglect the solution? It seems like a valid solution as long as the (three-space) momentum is not zero... And why isn't this state observed?

I'm reading in Griffiths' Introduction to Elementary Particles and there he derives the above, and in doing so he says (p233, on top) that e.g. the solution [itex]e^{-i p \cdot x} v^{(s)}[/itex] isn't allowed since it blows up as the three-space momentum [itex]\mathbf p \to 0[/itex]. However, why is this a sufficient reason to simply neglect the solution? It seems like a valid solution as long as the (three-space) momentum is not zero... And why isn't this state observed?