$W_{1+\infty}, Similarity Transformation and Interplay Between Integer and Fractional Quantum Hall Effect

Details $W_{1+\infty}, Similarity Transformation and Interplay Between Integer and Fractional Quantum Hall Effect $W_{1+\infty}, Similarity Transformation and Interplay Between Integer and Fractional Quantum Hall Effect

1994-04-15

arxiv.org/abs/hep-th/9404090v4

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, LaTex. ENSLAPP-A-466/94 (Revised version: some errors are corrected, references added, the assertion of quantum-mech

Scientific paper

We consider non-unitary similarity transformation, interconnecting the $W_{1+\infty}$ algebra representations for the fractional $\nu=\frac{1}{2p+1}$ and integer $\nu=1$ filling fractions. This transformation corresponds to the introduction of the complex abelian Chern-Simons gauge potentials, in terms of which the field-theoretic description of FQHE can be developed. The Jain's composite fermion approach and Lopez-Fradkin equivalence assertion are considered from the point of view of unitary and similarity transformations. As an application the second-quantized form of Laughlin function is derived.

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