Green's Function Approximation Method. II. The Polaron

Abstract

A method previously derived for the approximate construction of the nucleon Green's function is here applied to that of the polaron. After making an arbitrary translation of the phonon variables, a linear integral equation for the Green's function is derived by means of a symmetrical treatment and a noncorrelation assumption, in complete analogy to the nucleon problem. This equation is solved through the introduction of a spectral representation in the special case of zero total momentum. The lowest energy state of the system is calculated in terms of the arbitrary translations and then minimized with respect to them. Using the simplest nontrivial cutoff procedure to obtain the variational equation and its solution, results are obtained for values of the coupling parameter $\alpha <~3$, and are compared with those of Feynman.