On the Global Limiting Absorption Principle for Massless Dirac Operators

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

doi:10.1007/s00023-018-0675-5

On the Global Limiting Absorption Principle for Massless Dirac Operators

Alan Carey, Fritz Gesztesy^*, Jens Kaad, Galina Levitina, Roger Nichols, Denis Potapov, Fedor Sukochev

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

We prove a global limiting absorption principle on the entire real line for free, massless Dirac operators H₀= α· (- i∇) for all space dimensions n∈ N, n⩾ 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.

Original language	English
Pages (from-to)	1993-2019
Number of pages	27
Journal	Annales Henri Poincare
Volume	19
Issue number	7
DOIs	https://doi.org/10.1007/s00023-018-0675-5
Publication status	Published - 1 Jul 2018

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AU - Potapov, Denis

AU - Sukochev, Fedor

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AB - We prove a global limiting absorption principle on the entire real line for free, massless Dirac operators H0= α· (- i∇) for all space dimensions n∈ N, n⩾ 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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On the Global Limiting Absorption Principle for Massless Dirac Operators

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