Variational Statistical Mechanics in Terms of ``Observables'' for Normal and Superfluid Systems

Abstract

Thermodynamical functions are expressed by perturbation theory as stationary functionals of the 1‐, and 2‐body potentials; the stationary conditions yield the 1‐, and 2‐body correlation functions in terms of the potentials. Through the use of diagramatic methods, it is possible to explicitly invert these relations and express the potentials in terms of the correlation functions; in turn the thermo‐dynamical functions become stationary functionals of the correlation functions. This procedure is carried out for normal (quantum and classical) systems. For superfluid systems, $\frac{1}{2}\mathrm{-},\frac{3}{2}\mathrm{-}$ body potentials, and correlation functions need also be considered and the above procedure becomes imperative to eliminate the nonphysical $\frac{1}{2}\mathrm{-},\frac{3}{2}\mathrm{-}$ body potentials. Its first two steps are illustrated, and various features of this formulation and its usefulness are discussed.