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 algebras 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.
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