On the Global Limiting Absorption Principle for Massless Dirac Operators

TL;DR

This paper establishes a comprehensive limiting absorption principle for massless Dirac operators across all dimensions, including the two-dimensional case relevant to graphene, and proves self-adjointness for certain differential operators.

Contribution

It extends the limiting absorption principle to all space dimensions for massless Dirac operators, especially covering the two-dimensional case, and proves self-adjointness for related matrix-valued operators.

Findings

Limiting absorption principle proven for all dimensions n ≥ 2.

Application to two-dimensional case relevant to graphene.

Self-adjointness of first-order matrix operators with Lipschitz coefficients.

Abstract

We prove a global limiting absorption principle on the entire real line for free, massless Dirac operators $H_0 = \alpha \cdot (-i \nabla)$ for all space dimensions $n \in \mathbb{N}$, $n \geq 2$. This is a new result for all dimensions other than three, in particular, it applies to the two-dimensional case which is known to be of some relevance in applications to graphene. We also prove an essential self-adjointness result for first-order matrix-valued differential operators with Lipschitz coefficients.