A consistent RPA formalism
This paper examines the quasi-boson and generator-coordinate derivations of the RPA and concludes that they make uncritical and inconsistent use of the assumption that ground state correlations be small. It is proposed that consistent derivations of the RPA to various orders can be carried out by explicit retention of a certain power of a parameter γ which is proportional to the norm of the ground state correlations. To illustrate such a method, it is proved that a consistent, non-trivial, linear RPA theory exists only if the residual potential is small enough for first order perturbation theory to be valid.