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February 2005 Dirac-Weyl operators with a winding gauge potential
Tadahiro MIYAO
Hokkaido Math. J. 34(1): 185-218 (February 2005). DOI: 10.14492/hokmj/1285766204


Considered is a quantum system of $N(\ge2)$ charged particles moving in the plane ${\mathbb R}^2$ under the influence of a perpendicular magnetic field. Each particle feels the magnetic field concenrated on the positions of the other particles. The gauge potential which gives this magnetic field is called a winding gauge potential. Properties of the Dirac-Weyl operators with a winding gauge potential are investigated. Notions of local quantization and partial quantization are introduced to determine them. Especially, it is proven that existence of the zero-energy states of the Dirac-Weyl operators with a winding gauge potential is well determined by the local quantization and the partial quantization.


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Tadahiro MIYAO. "Dirac-Weyl operators with a winding gauge potential." Hokkaido Math. J. 34 (1) 185 - 218, February 2005.


Published: February 2005
First available in Project Euclid: 29 September 2010

zbMATH: 1069.81028
MathSciNet: MR2130778
Digital Object Identifier: 10.14492/hokmj/1285766204

Primary: 35J10
Secondary: 47B25, 47N50, 81Q10, 81Q60

Rights: Copyright © 2005 Hokkaido University, Department of Mathematics


Vol.34 • No. 1 • February 2005
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