  The formalism of density functional theory (DFT) can be easily extended to
the time dependent case (TDDFT). However, while in the static case the theory
is well established and is expected to be, at least in principle, an exact
approach for the determination of energy and density profiles of inhomogeneous
systems, the applicability of TDDFT to the investigation of dynamic phenomena
(for example propagation of collective phenomena) is less obvious especially in
the microscopic regime of large wave vectors. The purpose of this paper is to
discuss some relevant questions concerning the structure, the ingredients and
the applicability of TDDFT. Some emphasis will be also given to establish
important connections between TDDFT and microscopic theories such as the
Feynman theory for the elementary excitations of Bose superfluids.
