Noncommutative Geometry, Quantum Hall Effect and Berry Phase

Details Noncommutative Geometry, Quantum Hall Effect and Berry Phase Noncommutative Geometry, Quantum Hall Effect and Berry Phase

2003-08-06

arxiv.org/abs/hep-th/0308041v1

Physics

High Energy Physics

High Energy Physics - Theory

8 pages

Scientific paper

Taking resort to Haldane's spherical geometry we can visualize fractional quantum Hall effect on the noncommutative manifold $M_4 \times Z_N$ with $N>2$ and odd. The discrete space leads to the deformation of symplectic structure of the continuous manifold such that the symplectic area is given by $\triangle p.\triangle q=2\pi m \hbar$ with $m$ an odd integer which is related to the Berry phase and the filling factor is given by $\frac{1}{m}$. We here argue that this is equivalent to the noncommutative field theory as prescribed by Susskind and Polychronakos which is characterized by area preserving diffeomorphism. The filling factor $\frac{1}{m}$ is determined from the change in chiral anomaly and hence the Berry phase as envisaged by the star product.

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