Dirac operator zeromodes on a torus
Abstract
We study Dirac operator zeromodes on a torus for gauge background with uniform field strengths. Under the basic translations of the torus coordinates the wave functions are subject to twisted periodic conditions. In suitable torus coordinates the zeromode wave functions can be related to holomorphic functions of the complex torus coordinates. Half of the twisted boundary conditions for the holomorphic part of the zeromode wave function can be made periodic or antiperiodic. The remaining half is until coordinate dependent but diagonal. We completely solve the twisted boundary conditions and construct the zeromode wave functions. The chirality and the degeneracy of the zeromodes are uniquely determined by the gauge background and are consistent with the index theorem.
 Authors:
 Graduate School of Science and Engineering, Ibaraki University, Mito 3108512 (Japan)
 Department of Physics, Ibaraki University, Mito 3108512 (Japan)
 Department of Physics, Ibaraki University, Mito 3108512 (Japan). Email: fujiwara@mx.ibaraki.ac.jp
 Publication Date:
 OSTI Identifier:
 20976732
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Annals of Physics (New York); Journal Volume: 322; Journal Issue: 2; Other Information: DOI: 10.1016/j.aop.2006.02.013; PII: S00034916(06)000637; Copyright (c) 2006 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUNDARY CONDITIONS; CHIRALITY; COORDINATES; DIRAC OPERATORS; PERIODICITY; WAVE FUNCTIONS
Citation Formats
Tenjinbayashi, Yasushi, Igarashi, Hiroshi, and Fujiwara, Takanori. Dirac operator zeromodes on a torus. United States: N. p., 2007.
Web. doi:10.1016/j.aop.2006.02.013.
Tenjinbayashi, Yasushi, Igarashi, Hiroshi, & Fujiwara, Takanori. Dirac operator zeromodes on a torus. United States. doi:10.1016/j.aop.2006.02.013.
Tenjinbayashi, Yasushi, Igarashi, Hiroshi, and Fujiwara, Takanori. Thu .
"Dirac operator zeromodes on a torus". United States.
doi:10.1016/j.aop.2006.02.013.
@article{osti_20976732,
title = {Dirac operator zeromodes on a torus},
author = {Tenjinbayashi, Yasushi and Igarashi, Hiroshi and Fujiwara, Takanori},
abstractNote = {We study Dirac operator zeromodes on a torus for gauge background with uniform field strengths. Under the basic translations of the torus coordinates the wave functions are subject to twisted periodic conditions. In suitable torus coordinates the zeromode wave functions can be related to holomorphic functions of the complex torus coordinates. Half of the twisted boundary conditions for the holomorphic part of the zeromode wave function can be made periodic or antiperiodic. The remaining half is until coordinate dependent but diagonal. We completely solve the twisted boundary conditions and construct the zeromode wave functions. The chirality and the degeneracy of the zeromodes are uniquely determined by the gauge background and are consistent with the index theorem.},
doi = {10.1016/j.aop.2006.02.013},
journal = {Annals of Physics (New York)},
number = 2,
volume = 322,
place = {United States},
year = {Thu Feb 15 00:00:00 EST 2007},
month = {Thu Feb 15 00:00:00 EST 2007}
}

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