Translator Disclaimer
February 2005 Momentum operators with a winding gauge potential
Tadahiro MIYAO
Hokkaido Math. J. 34(1): 159-184 (February 2005). DOI: 10.14492/hokmj/1285766203


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 concenrated on the positions where the particle exsists. The gauge potential which gives this magnetic field is called a winding gauge potential. Properties of the momentum operators with a winding gauge potential are investigated. The momentum operators with a winding gauge potential are represented by the fibre direct integral of Arai's momentum operators [1]. Using this fibre direct integral decomposition, commutation properties of the momentum operators are investigated. A notion of local quantization of the magnetic flux is introduced to characterize the strong commutativity of the momentum operators. Aspects of the representation of the canonical commutation relations (CCR) are discussed. There is an interesting relation between the representation of the CCR with respect to this system and Arai's representation. Some applications of those results are also discussed.


Download Citation

Tadahiro MIYAO. "Momentum operators with a winding gauge potential." Hokkaido Math. J. 34 (1) 159 - 184, February 2005.


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

zbMATH: 1068.81039
MathSciNet: MR2130777
Digital Object Identifier: 10.14492/hokmj/1285766203

Primary: 81T13
Secondary: 47B25, 81Q10, 81S05

Rights: Copyright © 2005 Hokkaido University, Department of Mathematics


Vol.34 • No. 1 • February 2005
Back to Top