Spectral Flow for Dirac Operators with Magnetic Links
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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
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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