Strong convergence of wave operators for a family of Dirac operators

TL;DR

This paper investigates the asymptotic behavior of wave operators for a family of Dirac operators with varying potentials as a parameter h approaches infinity, establishing their strong convergence.

Contribution

It extends existing results on wave operators by analyzing their strong convergence for Dirac operators with potentials of fixed decay rates as the parameter h tends to infinity.

Findings

Wave operators exist and are complete for the family of Dirac operators.

Wave operators strongly converge as h approaches infinity.

The decay properties of potentials are independent of h.

Abstract

We consider a family of Dirac operators with potentials varying with respect to a parameter $h$. The set of potentials has different power-like decay independent of $h$. The proofs of existence and completeness of the wave operators are similar to that given in \cite{GAT}. We are mainly interested in the asymptotic behavior of the wave operators as $h\to\infty$.