- #1
Higgsy
- 18
- 0
On page 235 of srednicki (print) it says to plug a solution of the form $$ \textbf{$\Psi$} (x) = u(\textbf{p})e^{ipx} + v(\textbf{p})e^{-ipx}$$ into the dirac equation $$ (-i\gamma^{\mu} \partial_{\mu}+m)\textbf{$\Psi$}=0 $$
To get
$$(p_{\mu}\gamma^{\mu} + m)u(\textbf{p})e^{ipx} + (-p_{\mu}\gamma^{\mu} + m)v(\textbf{p})e^{-ipx} = 0 $$
I'm wondering what the reasoning for this term is (not wrt negative or positive but simply why p) $$p_{\mu}\gamma^{\mu}$$
To get
$$(p_{\mu}\gamma^{\mu} + m)u(\textbf{p})e^{ipx} + (-p_{\mu}\gamma^{\mu} + m)v(\textbf{p})e^{-ipx} = 0 $$
I'm wondering what the reasoning for this term is (not wrt negative or positive but simply why p) $$p_{\mu}\gamma^{\mu}$$