  Hartree-Fock theory has been justified as a mean-field approximation for
fermionic systems. However, it suffers from some defects in predicting physical
properties, making necessary a theory of quantum correlations. Recently,
bosonization of many-body correlations has been rigorously justified as an
upper bound on the correlation energy at high density with weak interactions.
We review the bosonic approximation, deriving an effective Hamiltonian. We then
show that for systems with Coulomb interaction this effective theory predicts
collective excitations (plasmons) in accordance with the random phase
approximation of Bohm and Pines, and with experimental observation.
