LINKS BETWEEN THE QUANTUM HALL EFFECT, CHIRAL BOSON THEORIES AND STRING THEORY

Chiral boson theory is introduced and its relevance to the quantum Hall effect is explained. It is shown that the chiral boson theory admits mode expansions which are essentially those which appear and are made use of in bosonic string theories. This immediately leads to a way of quantizing the theory. Restrictions on various parameters appearing in the model can be imposed in a natural way. Finally, it is suggested that some of these ideas have important applications to other geometries which could give rise to new types of physical behavior.

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Higher-Dimensional Quantum Hall Effect in String Theory

10.2172/799919 ◽

2002 ◽

Author(s):

Michal Fabinger

Keyword(s):

String Theory ◽

Hall Effect ◽

Quantum Hall Effect ◽

Quantum Hall ◽

Higher Dimensional

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THE CHIRAL BOSON THEORY AND EDGE STATES IN THE QUANTUM HALL EFFECT

Modern Physics Letters A ◽

10.1142/s0217732393001021 ◽

1993 ◽

Vol 08 (14) ◽

pp. 1297-1303 ◽

Cited By ~ 2

Author(s):

YUN SOO MYUNG

Keyword(s):

Hall Effect ◽

Landau Level ◽

Quantum Hall Effect ◽

Condensed Matter ◽

Quantum Hall ◽

Electron System ◽

Wave Functions ◽

Edge States ◽

Lowest Landau Level ◽

Boson Theory

We construct the wave functions for the edge states of a droplet of quantum Hall effect by performing the Gupta-Bleuler quantization of a chiral boson. These wave functions describe the chiral edge states of a many-electron system in the lowest Landau level. This demonstrates a crucial connection between the particle and condensed matter physics.

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SYMPLECTIC DEFORMATIONS, NONCOMMUTATIVE SCALAR FIELDS AND FRACTIONAL QUANTUM HALL EFFECT

International Journal of Modern Physics A ◽

10.1142/s0217751x08040433 ◽

2008 ◽

Vol 23 (16n17) ◽

pp. 2591-2612 ◽

Cited By ~ 5

Author(s):

M. DAOUD ◽

A. HAMAMA

Keyword(s):

Hall Effect ◽

Quantum Hall Effect ◽

Quantum Hall ◽

Scalar Fields ◽

Fractional Quantum Hall Effect ◽

Fractional Quantum ◽

Quantum Theories ◽

Fractional Quantum Hall ◽

Boson Theory ◽

Boson Fields

We clearly show that the symplectic structures deformations lead, upon quantization, to quantum theories of noncommutative fields. Two variants of deformations are considered. The quantization is performed and the modes expansions of the quantum fields are derived. The Hamiltonians are given and the degeneracies lifting induced by the deformation is also discussed. As an illustration, we consider the noncommutative chiral boson fields in the context of fractional quantum Hall effect. A generalized fractional filling factor is derived and shown to reproduce the Jain Hall states. We also show that the coupling of left and right edge excitations of a quantum Hall sample, gives rise a noncommutative chiral boson theory. The coupling or the noncommutativity induces a shift of the chiral components velocities. A nonlinear dispersion relation is obtained, corroborating some recent analytical and numerical analysis.

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