Renewal approach for the energy-momentum relation of the Fr\"ohlich polaron

Abstract

We study the qualitative behaviour of the energy-momentum relation of the Fr\"ohlich polaron at fixed coupling strength. Among other properties, we show that it is non-decreasing and that the correction to the quasi-particle energy is negative. We give a proof that the effective mass lies in $(1, \infty)$ that does not need the validity of a central limit theorem for the path measure.