  Today, most application of time-dependent density functional theory (TDDFT)
use adiabatic exchange-correlation (XC) potentials that do not take into
account non-local temporal effects. Incorporating such "memory" terms into XC
potentials is complicated by the constraint that the derived force and torque
densities must integrate to zero at every instance. This requirement can be met
by deriving the potentials from an XC action that is Galilean in-variant (GI).
We develop a class of simple but flexible forms for an action that respect
these constraints. The basic idea is to formulate the action in terms of the
Eularian-Lagrangian transformation (ELT) metric tensor, which is itself GI. The
general form of the XC potentials in this class is then derived and the linear
response limit is derived as well.
