The logical structure and the basic theorems of time-dependent current
density functional theory (TDCDFT) are analyzed and reconsidered from the point
of view of recently proposed time-dependent deformation functional theory
(TDDefFT). It is shown that the formalism of TDDefFT allows to avoid a
traditional external potential-to-density/current mapping. Instead the theory
is formulated in a form similar to the constrained search procedure in the
ground state DFT. Within this formulation of TDCDFT all basic functionals
appear from the solution of a constrained universal many-body problem in a
comoving reference frame, which is equivalent to finding a conditional extremum
of a certain universal action functional. As a result the physical origin of
the universal functionals entering the theory, as well as their proper causal
structure becomes obvious. In particular, this leaves no room for any doubt
concerning predictive power of the theory.Comment: revtex4, 24 page
