Werner Fischer, Hajo Leschke and Peter Müller,
How to get a lower bound on the polaron ground-state energy from the path-integral representation?,
in Path Integrals in Physics, edited by V. Sa-yakanit, J.-O. Berananda, W. Sritrakool (World Scientific, Singapore, 1994), pp. 347-354.

Abstract

A lower bound on the polaron ground-state energy is derived from the path-integral representation. This bound can be expressed in terms of the Euclidean propagator of the hydrogen atom. While the weak-coupling and strong-coupling limit can be investigated analytically, the intermediate-coupling regime requires a numerical treatment. Unfortunately, the results show that the bound is inferior to the only other available lower bound which is due to Lieb and Yamazaki. However, there is some hope that the proposed strategy for obtaining lower bounds is able to yield more stringent results.


Peter Müller