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 › Journal article › Research › peer-review

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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
Journal	Annales Henri Poincare
Volume	19
Issue number	7
Pages (from-to)	1993-2019
ISSN	1424-0637
DOIs	https://doi.org/10.1007/s00023-018-0675-5
Publication status	Published - 2018

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Carey, A., Gesztesy, F., Kaad, J., Levitina, G., Nichols, R., Potapov, D., & Sukochev, F. (2018). On the Global Limiting Absorption Principle for Massless Dirac Operators. Annales Henri Poincare, 19(7), 1993-2019. https://doi.org/10.1007/s00023-018-0675-5

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title = "On the Global Limiting Absorption Principle for Massless Dirac Operators",

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.",

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AU - Carey, Alan

AU - Gesztesy, Fritz

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AU - Levitina, Galina

AU - Nichols, Roger

AU - Potapov, Denis

AU - Sukochev, Fedor

PY - 2018

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N2 - 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.

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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DO - 10.1007/s00023-018-0675-5

M3 - Journal article

AN - SCOPUS:85045455404

VL - 19

SP - 1993

EP - 2019

JO - Annales Henri Poincare

JF - Annales Henri Poincare

SN - 1424-0637

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Documents & Links

10.1007/s00023-018-0675-5

On the Global Limiting Absorption Principle for Massless Dirac OperatorsSubmitted manuscript, 253 KB

http://arxiv.org/pdf/1711.01029