An analogue of the Sommerfeld radiation condition for the Dirac operator

TL;DR

This paper introduces a new radiation condition for the Dirac operator that enables the derivation of a Cauchy integral formula analogue in unbounded domains, using quaternionic analysis techniques.

Contribution

It proposes a simple radiation condition for the Dirac operator, facilitating integral formula derivation in unbounded domains, which is a novel approach in quaternionic analysis.

Findings

Established a radiation condition for Dirac spinors at infinity.

Proved an analogue of the Cauchy integral formula for the Dirac equation.

Utilized quaternionic analysis methods to achieve these results.

Abstract

A simple radiation condition at infinity for time-harmonic massive Dirac spinors is proposed. This condition allows an analogue of the Cauchy integral formula in unbounded domains for null-solutions of the Dirac equation to be proved. The result is obtained with the aid of methods of quaternionic analysis.