Renewal approach for the energy–momentum relation of the Fröhlich polaron

Abstract

We study the qualitative behaviour of the energy–momentum relation of the Fröhlich 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.