Green Function Method for Electron Gas. I

The Green function method is applied to the problems of electron gas. It is emphasized that there is a perfect parallelism between the Green function methods in zero-temperature problems and in finite-temperature problems of systems in thermal equilibrium. Further it is pointed out that the Green function method is also useful for the calculation of transport quantities. 1. Introduction Much advances have been made recently in the study of many-body problems in quantum mechanics and quantum statistics. Particularly noteworthy is the computation of the exact correlation energy of an electron gas at high density by Gell-Mann and Bruecknerl) (GB). The high density result of GB has subsequently been derived by other methods by Sawada et al}) Hubbard,3) and others.4) The field theoretical techniques are quite useful in summing certain subseries of terms in the so-called "linked-cluster expansion". Recently Galickij and Migdal,5) and Klein and Prahge 6