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2007

Interacting Quantum Topologies and the Quantum Hall Effect

Balachandran, A. P., Gupta, Kumar S., Kurkcuoglu, Seckin

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The algebra of observables of planar electrons subject to a constant background magnetic field B is given by A_theta(R^2) x A_theta(R^2) the product of two mutually commuting Moyal algebras.

It describes the free Hamiltonian and the guiding centre coordinates.
We argue that A_theta(R^2) itself furnishes a representation space for the actions of these two Moyal algebras, and suggest physical arguments for this choice of the representation space.
We give the proper setup to couple the matter fields based on A_theta(R^2) to electromagnetic fields which are described by the abelian commutative gauge group G_c(U(1)), i.e.

Interacting Quantum Topologies and the Quantum Hall Effect · Around

Built on

Z. F. Ezawa, Quantum Hall Effects
2000
Earlier work this paper cites.
R. Oeckl, Untwisting noncommutative R d R^{d} and the equivalence of quantum field theories,
2000
Earlier work this paper cites.

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A. P. Balachandran, A. Pinzul, B. A. Qureshi, S. Vaidya “Poincare invariant gauge and gravity theories on the Groenewold-Moyal plane,” arXiv:hep-th/0608138
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J. Wess, ”Deformed coordinate spaces: Derivatives”, hep-th/0408080
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Then

A. P. Balachandran, G. Mangano, A. Pinzul, and S. Vaidya, Spin and statistics on the Groenwald-Moyal plane: Pauli-forbidden levels and transitions,
2006
Later among the works it cites.
A. P. Balachandran, T. R. Govindarajan, G. Mangano, A. Pinzul, B. A. Qureshi and S. Vaidya, “Statistics and UV-IR mixing with twisted Poincare invariance,” Phys. Rev. D 75
2007
Closest in time.

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