On the Global Limiting Absorption Principle for Massless Dirac Operators

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 $n\in \mathbb{N}$, $n\ge 2$. 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.

22 pages

References in corpus (3)

• The Dirac equation in two dimensions: Dispersive estimates and classification of threshold obstructions
• Trace Formulas for a Class of non-Fredholm Operators: A Review
• Essential self-adjointness of powers of first-order differential operators on non-compact manifolds with low-regularity metrics

Cited by in corpus (5)

• Limiting absorption principle and Strichartz estimates for Dirac operators in two and higher dimensions
• On the one dimensional Dirac equation with potential
• Limiting absorption principle and scattering matrix for Dirac operators with $\delta$-shell interactions
• The Massless Dirac Equation in Three Dimensions: Dispersive estimates and zero energy obstructions
• Essential self-adjointness of symmetric first-order differential systems and confinement of Dirac particles on bounded domains in ${\mathbb{R}}^d$