Spectral Flow for Dirac Operators with Magnetic Links

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Standard

Spectral Flow for Dirac Operators with Magnetic Links. / Portmann, Fabian; Sok, Jérémy; Solovej, Jan Philip.

I: Journal of Geometric Analysis, Bind 30, Nr. 1, 2020, s. 1100-1167.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Portmann, F, Sok, J & Solovej, JP 2020, 'Spectral Flow for Dirac Operators with Magnetic Links', Journal of Geometric Analysis, bind 30, nr. 1, s. 1100-1167. https://doi.org/10.1007/s12220-018-00128-5

APA

Portmann, F., Sok, J., & Solovej, J. P. (2020). Spectral Flow for Dirac Operators with Magnetic Links. Journal of Geometric Analysis, 30(1), 1100-1167. https://doi.org/10.1007/s12220-018-00128-5

Vancouver

Portmann F, Sok J, Solovej JP. Spectral Flow for Dirac Operators with Magnetic Links. Journal of Geometric Analysis. 2020;30(1):1100-1167. https://doi.org/10.1007/s12220-018-00128-5

Author

Portmann, Fabian ; Sok, Jérémy ; Solovej, Jan Philip. / Spectral Flow for Dirac Operators with Magnetic Links. I: Journal of Geometric Analysis. 2020 ; Bind 30, Nr. 1. s. 1100-1167.

Bibtex

@article{bb49e6f77d8140ca9574072e4b4fcae0,
title = "Spectral Flow for Dirac Operators with Magnetic Links",
abstract = "This paper is devoted to the study of the spectral properties of Dirac operators on the three-sphere with singular magnetic fields supported on smooth, oriented links. As for Aharonov–Bohm solenoids in the Euclidean three-space, the flux carried by an oriented knot features a 2 π-periodicity of the associated operator. For a given link, one thus obtains a family of Dirac operators indexed by a torus of fluxes. We study the spectral flow of paths of such operators corresponding to loops in this torus. The spectral flow is in general nontrivial. In the special case of a link of unknots, we derive an explicit formula for the spectral flow of any loop on the torus of fluxes. It is given in terms of the linking numbers of the knots and their writhes.",
keywords = "Dirac operators, Knots, Links, Seifert surface, Spectral flow, Zero modes",
author = "Fabian Portmann and J{\'e}r{\'e}my Sok and Solovej, {Jan Philip}",
year = "2020",
doi = "10.1007/s12220-018-00128-5",
language = "English",
volume = "30",
pages = "1100--1167",
journal = "Journal of Geometric Analysis",
issn = "1050-6926",
publisher = "Springer",
number = "1",

}

RIS

TY - JOUR

T1 - Spectral Flow for Dirac Operators with Magnetic Links

AU - Portmann, Fabian

AU - Sok, Jérémy

AU - Solovej, Jan Philip

PY - 2020

Y1 - 2020

N2 - This paper is devoted to the study of the spectral properties of Dirac operators on the three-sphere with singular magnetic fields supported on smooth, oriented links. As for Aharonov–Bohm solenoids in the Euclidean three-space, the flux carried by an oriented knot features a 2 π-periodicity of the associated operator. For a given link, one thus obtains a family of Dirac operators indexed by a torus of fluxes. We study the spectral flow of paths of such operators corresponding to loops in this torus. The spectral flow is in general nontrivial. In the special case of a link of unknots, we derive an explicit formula for the spectral flow of any loop on the torus of fluxes. It is given in terms of the linking numbers of the knots and their writhes.

AB - This paper is devoted to the study of the spectral properties of Dirac operators on the three-sphere with singular magnetic fields supported on smooth, oriented links. As for Aharonov–Bohm solenoids in the Euclidean three-space, the flux carried by an oriented knot features a 2 π-periodicity of the associated operator. For a given link, one thus obtains a family of Dirac operators indexed by a torus of fluxes. We study the spectral flow of paths of such operators corresponding to loops in this torus. The spectral flow is in general nontrivial. In the special case of a link of unknots, we derive an explicit formula for the spectral flow of any loop on the torus of fluxes. It is given in terms of the linking numbers of the knots and their writhes.

KW - Dirac operators

KW - Knots

KW - Links

KW - Seifert surface

KW - Spectral flow

KW - Zero modes

UR - http://www.scopus.com/inward/record.url?scp=85074532755&partnerID=8YFLogxK

U2 - 10.1007/s12220-018-00128-5

DO - 10.1007/s12220-018-00128-5

M3 - Journal article

AN - SCOPUS:85074532755

VL - 30

SP - 1100

EP - 1167

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

SN - 1050-6926

IS - 1

ER -

ID: 230392825