Diagrams in the polaron model

Perturbation theory for the energy of a moving polaron is presented systematically on the basis of diagram technique. The rules formulated for constructing the Feynman diagrams make it possible to calculate the polaron energy to the terms of third order in the coupling constant. Analogous calculations are made for the mean number of virtual phonons. The obtained expansions have, respectively, the form $E/\omega=-\alpha-1,591962(\alpha/10)^2-0,806(\alpha/10)^3+\dots$ and $N=\alpha/2+3,183924(\alpha/10)^2+2,82(\alpha/10)^3+\dots$.