Annalen der Physik

Cover image for Vol. 18 Issue 5

May 2009

Volume 18, Issue 5

Pages 283–377

  1. Cover Picture

    1. Top of page
    2. Cover Picture
    3. Contents
    4. Original Paper
    1. Cover Picture: Ann. Phys. 5/2009

      Article first published online: 5 MAY 2009 | DOI: 10.1002/andp.200990005

  2. Contents

    1. Top of page
    2. Cover Picture
    3. Contents
    4. Original Paper
    1. Contents: Ann. Phys. 5/2009 (page 283)

      Article first published online: 5 MAY 2009 | DOI: 10.1002/andp.200918005

  3. Original Paper

    1. Top of page
    2. Cover Picture
    3. Contents
    4. Original Paper
    1. Quantum field theory and composite fermions in the fractional quantum Hall effect (pages 285–377)

      M. Kossow

      Article first published online: 5 MAY 2009 | DOI: 10.1002/andp.200910350

      Thumbnail image of graphical abstract

      A composite fermion model for the fractional quantum Hall effect is derived from relativistic quantum electrodynamics. With simple arguments it is shown that a special Chern Simons transformation of the Dirac electrons in four spacetime dimensions leads in the low energy limit to a single particle Hamiltonian for composite fermions in three dimensions with correction terms such as Rashba- or Dresselhaus-spin-orbit coupling and zitterbewegung. Furthermore a mechanism to quantum-mechanically project the quantum fields defined in the four dimensional Minkowski space to three dimensions is provided. This leads to a relativistic field theory and especially a composite fermion field theory in three dimension. This projection map can be combined with the projection onto a Landau level or composite fermion Landau level respectively. This results in a quasi relativistic quantum field theory on a noncommutative plane. The phenomenological models resulting from this approach are discussed and allow a systematical exploration of the effects of the spin and the condensation in a Landau level. From the relativistic approach corrections in terms of spin-orbit coupling effects are expected. From the projection onto Landau levels a modification of the dispersion relation and a modified composite fermion mass are expected. Furthermore, the BRST quantization for Chern Simons theories with compact gauge group is reviewed and the phenomenological consequences within a composite fermion model with spin are discussed. The connection to Wess Zumino Witten theories is recalled and a possible link between the corresponding central charge of the related affine Lie algebra and the composite fermion filling factor is pointed out.

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