# Hokkaido Mathematical Journal

## Hokkaido Mathematical Journal, 34 (2005) pp.185-218

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### Abstract

Considered is a quantum system of $N(\ge2)$ charged particles moving in the plane $\Ma{R}^2$ 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.

MSC(Primary) 35J10 81Q10, 47N50, 81Q60, 47B25 Dirac-Weyl operators with a winding gauge potential, strong anticommutativity,decomposable operator