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arXiv · 1711.01029

On the Global Limiting Absorption Principle for Massless Dirac Operators

Alan Carey·Fritz Gesztesy·Jens Kaad·Galina Levitina·Roger Nichols·Denis Potapov·Fedor Sukochev
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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.

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Alan Carey, Fritz Gesztesy, Jens Kaad, Galina Levitina, Roger Nichols, Denis Potapov, Fedor Sukochev. 2017-11-03. On the Global Limiting Absorption Principle for Massless Dirac Operators. https://doi.org/10.1007/s00023-018-0675-5

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