The Strong-Coupling Polaron in Electromagnetic Fields

This paper is concerned with Fr"ohlich polarons subject to external electromagnetic fields in the limit of large electron-phonon coupling. To leading order in the coupling constant, $\sqrt{\alpha }$, the ground state energy is shown to be correctly given by the minimum of the Pekar functional including the electromagnetic fields, provided these fields in the Fr"ohlich model are scaled properly with $\alpha$. As a corollary, the binding of two polarons in strong magnetic fields is obtained.