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 \(n \in {{\mathbb {N}}}\), \(n \geqslant 2\). 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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Communicated by Jan Derezinski.
A.C., G.L., and F.S. gratefully acknowledge financial support from the Australian Research Council. J.K. is supported by the DFF-research project 2 “Automorphisms and invariants of operator algebras,” no. 7014-00145B and by the Villum foundation (Grant 7423).
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Carey, A., Gesztesy, F., Kaad, J. et al. On the Global Limiting Absorption Principle for Massless Dirac Operators. Ann. Henri Poincaré 19, 1993–2019 (2018). https://doi.org/10.1007/s00023-018-0675-5
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DOI: https://doi.org/10.1007/s00023-018-0675-5