The Polaron Problem

Abstract

The study of the physical properties of a particle interacting with a quantum medium is common to many branches of physics. A classic example of this kind is the Fröhlich model of the polaron, — an electron moving with the polarization distortion of ions in an crystal. Polaron’s popularity as a model is due to its similarity to many field-theoretical constructions where bosons couple linearly to fermions (the meson-nucleon interactions inside nuclei, the “dressing” of quarks in the nonperturbative vacuum of QCD et cet.). The polaron problem is treated most straightforwardly in the PI formalism which allows one to reduce this problem to an effective one-particle task and, leads to new results not given by other conventional techniques. However, despite its long history and importance, the exact solution of the Fröhlich Hamiltonian is still lacking due to a high nonlocality (in time) and a Coulomb-like singularity in the polaron action. The application of the GER method to the d-dimensional polaron in this chapter results in highly accurate estimations of the main quasi-particle characteristic of the polaron — its ground-state energy.