= Advanced Green function
{title2=$G_A(t,t')=0\quad(t>t')$}
An <advanced Green function> has support only before its source time. It is selected by a future <boundary condition>, rather than an initial causal response. For $L=\partial_t^2+2\lambda\partial_t+\omega_0^2$ with $\lambda<0$ and $\Omega^2=\omega_0^2-\lambda^2>0$, the real-axis inverse <Fourier transform> of $(-\omega^2-2i\lambda\omega+\omega_0^2)^{-1}$ is $-H(-t)e^{-\lambda t}\sin(\Omega t)/\Omega$. Its first derivative jumps by one at zero. A growing retarded solution exists with a different inverse <contour>; this illustrates <causality versus stability of a Green function>.
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