By using the Bloch-Nordsieck method the self-energy of a polaron has been investigated in two limiting cases: (i) when the polaron velocity is low, i.e., $m{v}^2<\hslash \omega$, and (ii) when the velocity is high, i.e., $m{v}^2>\hslash \omega$. In case (i), this method gives results which are no better than those obtained by the use of the customary second-order perturbation theory, when the coupling constant is large. The contribution of the phonons of large momenta, if not more, is at least as much as that of the phonons of low momenta. However, in case (ii), we hope that our results are more satisfactory in view of the fact that the assumptions of the B-N method are better justified. In this case the self-energy is found to vary inversely as the velocity.

• Received 27 July 1953

DOI:https://doi.org/10.1103/PhysRev.94.38