Analysis of causality in time-dependent density-functional theory

It is pointed out that the kernel of the inverse response function delta v( r,t)/delta p(r',t'), whose existence is guaranteed by the Runge-Gross theor em, cannot Vanish for t<t'. As such the kernel f(xc), which is the function al derivative of the time-dependent exchange-correlation potential with res pect to the density, can be symmetric with respect to an interchange betwee n t and t' without violating causality. Thus there is no conflict between t he symmetry requirement of this kernel and causality in time-dependent dens ity-functional theory.