= Retarded unit-frequency oscillator response
{title2=$G_R(t)=\Theta(t)\sin t$}
The <retarded Green function> for $d^2/dt^2+1$ is $G_R(t)=\Theta(t)\sin t$, with <Fourier transform> $[1-(\omega+i0^+)^2]^{-1}$ in the $e^{-i\omega t}$ convention. Both poles lie below the real axis. Convolution with a force gives the solution with no incoming homogeneous oscillation. A source that is nonzero at negative times can have a nonzero response before a chosen zero of time without violating <causality>.
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