Scaling theory of dynamic scattering centers and moving heavy particles in a fermionic environment.

Abstract

A dynamic scattering object and the slowly building screening fermion cloud around it are examined. The models previously studied for strong on-site scattering---x-ray absorption, the anisotropic Kondo problem, the Anderson model, etc.---have the common feature that all values of the bare scattering matrix commute with one another. Nozi\`eres and De Dominicis's path-integral method can be applied directly to these problems because the scatterings in different channels are independent. The aim of this paper is to extend the theory to those problems, in which the scattering matrix has noncommuting values as, e.g., in the case of a scattering center moving in real space. Integrating over the fermionic degrees of freedom, we get to the problem of a one-dimensional dielectric medium with moving domain walls. In contrast to the commutative case, more-than-two-particle interactions may arise between the domain walls. Renormalization is carried out by keeping the terms that are the most divergent in the short-time-cutoff parameter.