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I have a question regarding the construction of solutions to the Diracequation for generell [itex] \vec{p} [/itex]. In my lecturenotes (and also in Itzykson/Zuber) it is stated that it is easier than boosting the restframe-solutions, to construct them by using [tex] (\gamma^{\mu}p_{\mu}+m)(\gamma^{\nu}p_{\nu}-m)=0 [/tex] But how does that help me? Why do I get the appropriate solution if I operate on the restfram-solution with the Diracoperator: [tex] u^{\alpha}(p)=\frac{1}{N}(\gamma^{\mu}p_{\mu}+m)u^{\alpha}(m,\vec{0})[/tex]

Where [tex]

u^{1}(m,\vec{0})=\left(\begin{array}{c}1\\0\\0\\0\end{array}\right) [/tex] and

[tex] u^{2}(m,\vec{0})=\left(\begin{array}{c}0\\1\\0\\0\end{array}\right) [/tex]

Thanks for your help!

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# I Solution to the Dirac equation

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