Resonances for the radial Dirac operators

TL;DR

This paper investigates the resonances of the radial Dirac operator with compactly supported potentials, analyzing their distribution, asymptotics, and deriving a trace formula in the massless case.

Contribution

It provides new results on the asymptotic distribution of resonances and establishes a trace formula for the massless radial Dirac operator.

Findings

Asymptotics of the resonance counting function

Resonance distribution properties

Trace formula in the massless case

Abstract

We consider the radial Dirac operator with compactly supported potentials. We study resonances as the poles of scattering matrix or equivalently as the zeros of modified Fredholm determinant. We obtain the following properties of the resonances: 1) asymptotics of counting function, 2) in the massless case we get the trace formula in terms of resonances.