Towards a variational theory for RPA-like correlations and fluctuations

Random phase theory (RPA) is generalised in such a way that it obeys a Ritz variational principle for the ground-state energy. The wave function is not to be constructed explicitly; instead an equivalent nonlinear set of equations for the two-particle density matrix is obtained. For practical applications, at some point a truncation scheme has to be introduced. We give arguments that the proposed truncation scheme should converge quickly and indeed it does so in an application of our theory to the Lipkin model. In addition, a generalised single-particle equation which couples to the RPA solution is introduced. (orig.)