Level Quantization for the Noncommutative Chern-Simons Theory

Nair, V. P.; Polychronakos, Alexios P.

doi:10.1103/physrevlett.87.030403

Cited by 130 publications

(187 citation statements)

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“…This result have also been observed using another calculational method [31]. We note that our result and also our arguments heavily rely on non-zero θ, furthermore the limit θ → 0 is not a smooth one.…”

Section: The Ncu(n) Winding Numbersupporting

confidence: 64%

A note on noncommutative Chern–Simons theories

Sheikh-Jabbari¹

2001

Physics Letters B

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The three dimensional Chern-Simons theory on R 2 θ × R is studied. Considering the gauge transformations under the group elements which are going to one at infinity, we show that under arbitrary (finite) gauge transformations action changes with an integer multiple of 2π if, the level of noncommutative Chern-Simons is quantized. We also briefly discuss the case of the noncommutative torus and some other possible extensions.

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Section: The Ncu(n) Winding Numbersupporting

confidence: 64%

A note on noncommutative Chern–Simons theories

Sheikh-Jabbari¹

2001

Physics Letters B

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“…The Gauss law constraint quantum mechanically becomes a statement on the allowed representations of the generators of the conjugation symmetry of w, w † . Group theory constraints require the quantization condition [37,38,6] …”

Section: Quantizationmentioning

confidence: 99%

Fractional quantum Hall effect on the two-sphere: A matrix model proposal

Morariu

Polychronakos

2005

Phys. Rev. D

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“…These effects might arise as a noncommutative version of Quantum Mechanics, NCQM, which lately has also been the focus of a lively discussion in the literature [4,9,10,11,12,13].…”

Section: Introductionmentioning

confidence: 99%

Noncommutative gravitational quantum well

et al. 2005

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We study noncommutative geometry at the Quantum Mechanics level by means of a model where noncommutativity of both configuration and momentum spaces is considered. We analyze how this model affects the problem of the two-dimensional gravitational quantum well and use the latest experimental results for the two lowest energy states of neutrons in the Earth's gravitational field to establish an upper bound on the fundamental momentum scale introduced by noncommutativity, namely √ η 1 meV/c, a value that can be improved in the future by up to 3 orders of magnitude. We show that the configuration space noncommutativity has, in leading order, no effect on the problem. We also analyze some features introduced by the model, specially a correction to the presently accepted value of Planck's constant to 1 part in 10 24 .

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Level Quantization for the Noncommutative Chern-Simons Theory

Abstract: We show that the coefficient of the three-dimensional Chern-Simons action on the noncommutative plane must be quantized. Similar considerations apply in other dimensions as well.

Cited by 130 publications

References 3 publications

A note on noncommutative Chern–Simons theories

A note on noncommutative Chern–Simons theories

Fractional quantum Hall effect on the two-sphere: A matrix model proposal

Noncommutative gravitational quantum well

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