Scaling relations between the two- and three-dimensional polarons for static and dynamical properties

Scaling relations are presented which allow one to obtain static and dynamical physical quantities of the two-dimensional (2D) polaron out of known results for the 3D polaron. These scaling relations are exact within second-order perturbation theory and are approximately valid (on a 1% level) for higher orders in the electron-phonon coupling constant. A formal generalization of these scaling relations to the n-dimensional polaron is given.