Elementary arguments that the Wu–Austin Hamiltonian has no finite ground state (the search for a microscopic foundation of Fröhlichs theory)

Abstract

The Wu–Austin Hamiltonian as the basis for deriving Fröhlichs rate equations from a microscopical point of view has been investigated. In addition to an earlier paper we show in a very easy manner that this or similar Hamiltonians have no lower bound and are therefore unphysical. The perturbation expansion which is the tool to derive Fröhlichs rate equations with this Hamiltonian is not converging. Therefore, the usual derivation of this rate equation is not valid.