Product of Projective Representations in Description of Multi-Electron States in An External Magnetic Field |
| W. Florek Computational Physics Division, Institute of Physics Adam Mickiewicz University, Umultowska 85, 61-614 Poznań, Poland |
| Received: October 27, 1998; revised version February 1, 1999 |
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| In this paper all inequivalent irreducible projective representations of the two-dimensional translation group for a given factor system are determined. A normalized, i.e. corresponding to the Landau gauge, factor system is considered. Obtained representations directly lead to concept of magnetic cells and to periodicity with respect to the charge of a moving particle. It is also shown that the quantization condition is imposed on the product qH of the charge q and the magnitude of magnetic field H. The Kronecker product of such representations is considered and it is proven that the multiplication of representations corresponds to the addition of charges of particles moving in a given external magnetic field. In general, coupling of d representations corresponds to d-particle states. Presented results can be applied in any problem related to two-dimensional electron gas in a magnetic field, for example in the fractional quantum Hall effect or high temperature superconductivity. |
| DOI: 10.12693/APhysPolA.95.871 PACS numbers: 03.65.Fd, 02.10.Sp, 71.70.Di |