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Chose the "retarded" solution, such that the function is zero unless t>t'<br>
 
Chose the "retarded" solution, such that the function is zero unless t>t'<br>
 
<math>G(x,x')=\frac{1}{(2\pi)^4}\int d^3ke^{-i\mathbf{k}(x-x')}\int d(\frac{\omega}{c}) \frac{e^{i\omega(t-t')}}{(\frac{\omega}{c}-k)(\frac{\omega}{c}+k)}\Theta</math><br>
 
<math>G(x,x')=\frac{1}{(2\pi)^4}\int d^3ke^{-i\mathbf{k}(x-x')}\int d(\frac{\omega}{c}) \frac{e^{i\omega(t-t')}}{(\frac{\omega}{c}-k)(\frac{\omega}{c}+k)}\Theta</math><br>
 +
<math>=\frac{1}{(2\pi)^4}\int d^3ke^{-i\mathbf{k}(x-x')}(2\pi i  \frac{e^{ick(t-t')}-e^{-ick(t-t')}}{2k)})\Theta
 +
 +
</math>
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