Self-adjointness and spectral properties of Dirac operators with magnetic links

Fabian Portmann; Jérémy Sok; Jan Philip Solovej

doi:10.1016/j.matpur.2017.10.010

Self-adjointness and spectral properties of Dirac operators with magnetic links

Fabian Portmann, Jérémy Sok, Jan Philip Solovej

Department of Mathematical Sciences

4 Citations (Scopus)

3 Downloads (Pure)

Abstract

We define Dirac operators on S ³ (and R ³) with magnetic fields supported on smooth, oriented links and prove self-adjointness of certain (natural) extensions. We then analyze their spectral properties and show, among other things, that these operators have discrete spectrum. Certain examples, such as circles in S ³, are investigated in detail and we compute the dimension of the zero-energy eigenspace.

Original language	English
Journal	Journal de Mathematiques Pures et Appliquees
Volume	119
Pages (from-to)	114-157
ISSN	0021-7824
DOIs	https://doi.org/10.1016/j.matpur.2017.10.010
Publication status	Published - 2018

Keywords

math-ph
math.MP
81Q10 (Primary), 58C40, 57M25 (Secondary)

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10.1016/j.matpur.2017.10.010

https://arxiv.org/abs/1701.04987

Cite this

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title = "Self-adjointness and spectral properties of Dirac operators with magnetic links",

abstract = "We define Dirac operators on S 3 (and R 3) with magnetic fields supported on smooth, oriented links and prove self-adjointness of certain (natural) extensions. We then analyze their spectral properties and show, among other things, that these operators have discrete spectrum. Certain examples, such as circles in S 3, are investigated in detail and we compute the dimension of the zero-energy eigenspace. ",

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year = "2018",

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T1 - Self-adjointness and spectral properties of Dirac operators with magnetic links

AU - Portmann, Fabian

AU - Sok, Jérémy

AU - Solovej, Jan Philip

PY - 2018

Y1 - 2018

N2 - We define Dirac operators on S 3 (and R 3) with magnetic fields supported on smooth, oriented links and prove self-adjointness of certain (natural) extensions. We then analyze their spectral properties and show, among other things, that these operators have discrete spectrum. Certain examples, such as circles in S 3, are investigated in detail and we compute the dimension of the zero-energy eigenspace.

AB - We define Dirac operators on S 3 (and R 3) with magnetic fields supported on smooth, oriented links and prove self-adjointness of certain (natural) extensions. We then analyze their spectral properties and show, among other things, that these operators have discrete spectrum. Certain examples, such as circles in S 3, are investigated in detail and we compute the dimension of the zero-energy eigenspace.

KW - math-ph

KW - math.MP

KW - 81Q10 (Primary), 58C40, 57M25 (Secondary)

U2 - 10.1016/j.matpur.2017.10.010

DO - 10.1016/j.matpur.2017.10.010

M3 - Journal article

SN - 0021-7824

VL - 119

SP - 114

EP - 157

JO - Journal des Mathematiques Pures et Appliquees

JF - Journal des Mathematiques Pures et Appliquees

ER -

Self-adjointness and spectral properties of Dirac operators with magnetic links

Abstract

Keywords

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