Generalized scattering phase for long range perturbations of elliptic operators

Abstract

We show that limits on the real axis of arguments of regularized relative determinants for differential operators on $\text{R}{}^{\mathrm{d}}$, exist in the weak sense. We call these limits generalized scattering phases. They extend, in the case of long range perturbations, the usual definition of scattering phase given by Birman–Krein theory. In Euclidean scattering, we give high energy expansions under a non-trapping assumption.