The renormalized variational theory: Its structure,interpretation, and relation to other methods

We apply the Ritz variational principle to a renormalized form of the Iwamoto-Yamada cluster expansion, restricting our discussion to infinite systems. The structure of the resulting theory is governed by the renormalization which keeps track of the normalization denominator in the expectation value. The single-particle potential for hole states (u_i) is introduced as a Lagrange multiplier in the variational principle, and the self-consistent choice of u_i guarantees that the renormalization factors are determined correctly. The importance of the renormalization is illustrated by a discussion of the two-body approximation to our theory. The general formalism is evaluated in more detail for the representation Ψ_T = exp(S)Φ of the trial wave function. Very fundamental considerations show that the theory is especially adapted to that choice of Ψ_T. In addition, if we use that choice of Ψ_T the self-consistent single-particle energies are directly related to experiment, and the theory is almost identical to renormalized Brueckner theory. Thus we are able to clarify many aspects of the latter. We also discuss the relation to the theory of Coester and Kümmel.