  One-particle reduced density matrix functional theory would potentially be
the ideal approach for describing Bose-Einstein condensates. It namely replaces
the macroscopically complex wavefunction by the simple one-particle reduced
density matrix, therefore provides direct access to the degree of condensation
and still recovers quantum correlations in an exact manner. We eventually
initiate and establish this novel theory by deriving the respective universal
functional $\mathcal{F}$ for general homogeneous Bose-Einstein condensates with
arbitrary pair interaction. Most importantly, the successful derivation
necessitates a particle-number conserving modification of Bogoliubov theory and
a solution of the common phase dilemma of functional theories. We then
illustrate this novel approach in several bosonic systems such as homogeneous
Bose gases and the Bose-Hubbard model. Remarkably, the general form of
$\mathcal{F}$ reveals the existence of a universal Bose-Einstein condensation
force which provides an alternative and more fundamental explanation for
quantum depletion.
