= One-dimensional retarded wave Green function
{title2=$G_R(x,t)=\frac{\Theta(t-|x|/c)}{2c}$}
For $(\partial_t^2-c^2\partial_x^2)G_R=\delta(t)\delta(x)$, zero response before the impulse gives the displayed <retarded fundamental solution>. Its initial displacement is zero and its initial velocity is $\delta(x)$. The response fills the interior of the forward <causal cone for the constant-speed wave equation>, rather than living only on its boundary. Changing the overall sign of the differential operator changes the Green function's sign. Equivalently, the spatial <Fourier transform> is $\Theta(t)\sin(c|k|t)/(c|k|)$, whose inverse is a rectangular profile. Values assigned exactly on the wave fronts do not change the associated <distribution>.
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