  Given a vector space of microscopic quantum observables, density functional
theory is formulated on its dual space. A generalized Hohenberg-Kohn theorem
and the existence of the universal energy functional in the dual space are
proven. In this context ordinary density functional theory corresponds to the
space of one-body multiplication operators. When the operators close under
commutation to form a Lie algebra, the energy functional defines a Hamiltonian
dynamical system on the coadjoint orbits in the algebra's dual space. The
enhanced density functional theory provides a new method for deriving the group
theoretic Hamiltonian on the coadjoint orbits from the exact microscopic
Hamiltonian.
