Perturbation Theory for an Infinite Medium of Fermions. II

New forms of the linked cluster expansion for the ground-state energy of a normal spherical system are given in terms of the exact single-particle propagator and of the associated self-energy operator. These forms are shown to be stationary with respect to variations of the latter quantities. A new concise proof of the Hugenholtz-Van Hove theorem on single-particle energies is then possible. The variational principle also explains the insensitivity of recent binding energy calculations to the choice of single-particle energies. It is shown how all results may be extended to systems with anisotropic features.