The Fröhlich Polaron at Strong Coupling -- Part II: Energy-Momentum Relation and Effective Mass

We study the Fröhlich polaron model in ${\mathbb{R}}^3$, and prove a lower bound on its ground state energy as a function of the total momentum. The bound is asymptotically sharp at large coupling. In combination with a corresponding upper bound proved earlier, it shows that the energy is approximately parabolic below the continuum threshold, and that the polaron’s effective mass (defined as the semi-latus rectum of the parabola) is given by the celebrated Landau–Pekar formula. In particular, it diverges as ${\alpha }^4$ for large coupling constant $\alpha$.