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On the global limiting absorption principle for massless Dirac operators. (English) Zbl 1394.81115

Summary: 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.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81R20 Covariant wave equations in quantum theory, relativistic quantum mechanics
47A53 (Semi-) Fredholm operators; index theories
47B25 Linear symmetric and selfadjoint operators (unbounded)
82D80 Statistical mechanics of nanostructures and nanoparticles
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