Monotonicity of the Polaron Energy

In condensed matter physics, the polaron is described by the Hamiltonian of H. Fröhlich. In this paper, the Fröhlich Hamiltonian is investigated from a viewpoint of operator inequalities proposed in [36]. This point of view clarifies the monotonicity of polaron energy, i.e. denoting the lowest energy of the Fröhlich Hamiltonian with the ultraviolet cutoff Λ by EΛ, we prove that EΛ, > EΛ′ for Λ < Λ′.