# Limiting absorption principle and scattering matrix for Dirac operators with $\delta$-shell interactions

## TL;DR

This paper establishes a limiting absorption principle and analyzes the scattering matrix for Dirac operators with delta-shell interactions, advancing understanding of their spectral and scattering properties.

## Contribution

It introduces a limiting absorption principle and a scattering matrix representation for Dirac operators with delta-shell interactions, which was not previously available.

## Key findings

- Proves a limiting absorption principle for these operators.
- Shows completeness of wave operators.
- Provides a formula for the scattering matrix.

## Abstract

We provide a limiting absorption principle for self-adjoint realizations of Dirac operators with electrostatic and Lorentz scalar $\delta$-shell interactions supported on regular compact surfaces. Then we show completeness of the wave operators and give a representation formula for the scattering matrix.