The ground state energy of a polaron in a strong magnetic field

We show that the ground state of a polaron in a homogeneous magnetic field $B$ and its energy are described by an effective one-dimensional minimization problem in the limit $B\to \mathrm{\infty }$. This holds both in the linear Fr"ohlich and in the non-linear Pekar model and makes rigorous an argument of Kochetov, Leschke and Smondyrev.