Quantum corrections to the Pekar asymptotics of a strongly coupled polaron

We consider the Fr\"ohlich polaron model in the strong coupling limit. It is well known that to leading order the ground state energy is given by the (classical) Pekar energy. In this work, we establish the subleading correction, describing quantum fluctuation about the classical limit. Our proof applies to a model of a confined polaron, where both the electron and the polarization field are restricted to a set of finite volume, with linear size determined by the natural length scale of the Pekar problem.Comment: LaTeX, 40 pages; final version, to appear in Commun. Pure. Appl. Mat