Fractional quantum numbers, complex orbifolds and noncommutative geometry

Varghese Mathai; Graeme Peter Desmond Wilkin

doi:10.1088/1751-8121/ac0b8c

Fractional quantum numbers, complex orbifolds and noncommutative geometry

Varghese Mathai, Graeme Peter Desmond Wilkin

Mathematics

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

Abstract

This paper studies the conductance on the universal homology covering space Z of 2D orbifolds in a strong magnetic field, thereby removing the rationality constraint on the magnetic field in earlier works (Avron et al 1994 Phys. Rev. Lett. 73 3255–3257; Mathai and Wilkin 2019 Lett. Math. Phys. 109 2473–2484; Prieto 2006 Commun. Math. Phys. 265 373–396) in the literature. We consider a natural Landau Hamiltonian on Z and study its spectrum which we prove consists of a finite number of low-lying isolated points and calculate the von Neumann degree of the associated holomorphic spectral orbibundles when the magnetic field B is large, and obtain fractional quantum numbers as the conductance.

Original language	English
Article number	314001
Number of pages	18
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	54
DOIs	https://doi.org/10.1088/1751-8121/ac0b8c
Publication status	Published - 1 Jul 2021

Bibliographical note

© 2021 IOP Publishing Ltd. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details

Keywords

fractional quantum numbers
Riemann orbifolds
holomorphic orbibundles
von Neumann degree
noncommutative geometry

Access to Document

10.1088/1751-8121/ac0b8c

Orbifolds_and_NG
© 2021 IOP Publishing Ltd. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details
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Cite this

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