UV finite field theories on noncommutative spacetimes: The quantum Wick product and time independent perturbation theory

Kossow, Marcel

doi:10.1103/physrevd.77.065018

Cited by 5 publications

(3 citation statements)

References 12 publications

(36 reference statements)

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“…Therefore the dispersion relation (113) introduced in section 2 for the usual theory should be strongly modified due to the modified structure at the scale of the magnetic length and this has then consequences for the effective composite fermion masses (117). We also expect that the 'classical' results are reobtained in the large scale limit where the noncommutativity vanishes which is also true in some scalar field theories on noncommutative spacetimes [118]. In general this setup may provide a useful proper treatment of low energy composite fermions in a Landau, or composite fermion Landau level, which is needed also in the case of second generation composite fermions.…”

Section: Low Energy Effective Noncommutative Modelmentioning

confidence: 87%

Quantum field theory and composite fermions in the fractional quantum Hall effect

Kossow

2009

Annalen der Physik

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We derive a composite fermion model for the fractional quantum Hall effect 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 we provide a mechanism to quantum‐mechanically project the quantum fields defined in the four dimensional Minkowski space to three dimensions. 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. We expect from the relativistic approach corrections in terms of spin‐orbit coupling effects. From the projection onto Landau levels we expect a modification of the dispersion relation and a modified composite fermion mass. 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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Section: Low Energy Effective Noncommutative Modelmentioning

confidence: 87%

Quantum field theory and composite fermions in the fractional quantum Hall effect

Kossow

2009

Annalen der Physik

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Section: Low Energy Effective Noncommutative Modelmentioning

confidence: 95%

Quantum field theory and composite fermions in the fractional quantum Hall effect

Kossow¹

2009

Ann. Phys.

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We derive a composite fermion model for the fractional quantum Hall effect 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 we provide a mechanism to quantum-mechanically project the quantum fields defined in the four dimensional Minkowski space to three dimensions. 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. We expect from the relativistic approach corrections in terms of spin-orbit coupling effects. From the projection onto Landau levels we expect a modification of the dispersion relation and a modified composite fermion mass. 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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“…Note that UV finiteness does not mean that renormalisation is not needed at all: a finite renormalisation, with renormalisation constants depending on the Planck length, is needed, in order to subtract physically meaningless contributions; it should be possible to choose that dependence so that, applying this procedure to the usual renormalized interaction derived on the classical Minkowski space, the resulting perturbation expansion reproduces, in the limit λ P → 0, the usual renormalised perturbation expansion; however the interplay with the adiabatic limit and with the renormalised one particle states have to be considered; for progress on this line, see [75,76,77].…”

Section: Local Quantum Physics and The Measurement Processmentioning

confidence: 99%

The principle of locality: Effectiveness, fate, and challenges

Doplicher

2010

Journal of Mathematical Physics

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UV finite field theories on noncommutative spacetimes: The quantum Wick product and time independent perturbation theory

Cited by 5 publications

References 12 publications

Quantum field theory and composite fermions in the fractional quantum Hall effect

Quantum field theory and composite fermions in the fractional quantum Hall effect

Quantum field theory and composite fermions in the fractional quantum Hall effect

The principle of locality: Effectiveness, fate, and challenges

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