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On the Global Limiting Absorption Principle for Massless Dirac Operators

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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 \(n \in {{\mathbb {N}}}\), \(n \geqslant 2\). 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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Authors and Affiliations

  1. Mathematical Sciences Institute, Australian National University, Kingsley St., Canberra, ACT, 0200, Australia

    Alan Carey

  2. School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW, 2522, Australia

    Alan Carey

  3. Department of Mathematics, Baylor University, One Bear Place #97328, Waco, TX, 76798-7328, USA

    Fritz Gesztesy

  4. Department of Mathematics and Computer Science, University of Southern Denmark, Campusvej 55, 5230, Odense M, Denmark

    Jens Kaad

  5. School of Mathematics and Statistics, UNSW, Kensington, NSW, 2052, Australia

    Galina Levitina, Denis Potapov & Fedor Sukochev

  6. Mathematics Department, The University of Tennessee at Chattanooga, 415 EMCS Building, Dept. 6956, 615 McCallie Ave, Chattanooga, TN, 37403, USA

    Roger Nichols

Authors
  1. Alan Carey
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  2. Fritz Gesztesy
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  3. Jens Kaad
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  4. Galina Levitina
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  5. Roger Nichols
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  6. Denis Potapov
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  7. Fedor Sukochev
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Corresponding author

Correspondence to Fritz Gesztesy.

Additional information

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

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