  This article generalizes the notion of the local density of a many-body
system to introduce collective coordinates as explicit degrees of freedom. It
is shown that the energy of the system can be expressed as a functional of this
object. The latter can in turn be factorized as the product of the square of a
collective wave function and a normalized collective-coordinate-dependent
density. Energy minimization translates into a set of coupled equations, i.e. a
local Schr\"odinger equation for the collective wave function and a set of
Kohn-Sham equations for optimizing the normalized density at each point in the
collective space. These equations reformulate the many-body problem exactly
provided one is able to determine density- and
collective-wave-function-dependent terms of the collective mass and potential
which play a similar role to the exchange-correlation term in electronic
Kohn-Sham density functional theory.
