  It is shown that the exchange-correlation part of the action functional
$A_{xc}[\rho (\vec r,t)]$ in time-dependent density functional theory , where
$\rho (\vec r,t)$ is the time-dependent density, is invariant under the
transformation to an accelerated frame of reference $\rho (\vec r,t) \to \rho '
(\vec r,t) = \rho (\vec r + \vec x (t),t)$, where $\vec x (t)$ is an arbitrary
function of time. This invariance implies that the exchange-correlation
potential in the Kohn-Sham equation transforms in the following manner:
$V_{xc}[\rho '; \vec r, t] = V_{xc}[\rho; \vec r + \vec x (t),t]$. Some of the
approximate formulas that have been proposed for $V_{xc}$ satisfy this exact
transformation property, others do not. Those which transform in the correct
manner automatically satisfy the ``harmonic potential theorem", i.e. the
separation of the center of mass motion for a system of interacting particles
in the presence of a harmonic external potential. A general method to generate
functionals which possess the correct symmetry is proposed.
