On the absolutely continuous spectrum of Dirac operator

TL;DR

This paper proves that the massless Dirac operator in three-dimensional space with long-range potentials has an absolutely continuous spectrum covering the entire real line, including matrix-valued potential cases.

Contribution

It establishes the full real line spectrum for massless Dirac operators with long-range potentials, extending to matrix-valued cases.

Findings

The spectrum of the massless Dirac operator is absolutely continuous and covers all real numbers.

The result applies to Dirac operators with matrix-valued potentials.

The paper advances understanding of spectral properties of Dirac operators with long-range interactions.

Abstract

We prove that the massless Dirac operator in $\mathbb{R^3}$ with long-range potential has an a.c. spectrum which fills the whole real line. The Dirac operators with matrix-valued potentials are considered as well.