CONSTRAINTS ON NONCOMMUTATIVE HALL EFFECT REVISITED

2008 ◽  
Vol 23 (26) ◽  
pp. 4361-4370 ◽  
Author(s):  
CRESUS F. L. GODINHO
Keyword(s):  
Gauge Theory ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Hall Conductivity ◽  
Second Step ◽  
Direct Relation ◽  
General Constraints ◽  
Chern Simons

We consider a semiclassical formulation of the quantum Hall effect by means of an Chern–Simons gauge theory constructed for a Schrödinger field. We build up constraints managing the Faddeev–Jackiw algorithm and show a direct relation of the constraints with Hall conductivity. In the second step, we consider the noncommutative extension to the action computing the new and more general constraints and, as a right consequence, an interesting correction for the conductivity expression is found. Finally, we speculate possible interpretations of this new result and its consequences.

Chiral bosonic field theories and the quantum Hall effect

2001 ◽  
Vol 79 (9) ◽  
pp. 1121-1131 ◽  
Author(s):  
P Bracken
Keyword(s):  
Hall Effect ◽  
Gauge Transformation ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Equation Of Motion ◽  
Hall Conductivity ◽  
Field Theories ◽  
Bosonic Field ◽  
Chern Simons

The gauge-transformation properties of the actions of certain scalar and Chern–Simons theories are investigated, including contributions from the boundary. By imposing chirality constraints on the fields, these types of theories can be used to describe the quantum Hall effect. It is shown that the corresponding equation of motion for the associated current for the theory generates an anomaly, which can be related directly to the Hall conductivity. PACS Nos.: 73.43, 03.70, 11.10, 11.30R

WILSON LOOPS AND NON-ABELIAN STATISTICS IN THE QUANTUM HALL EFFECT

1992 ◽  
Vol 06 (17) ◽  
pp. 2875-2891
Author(s):  
MICHAEL STONE
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Conductivity Tensor ◽  
Hall Conductivity ◽  
Wilson Loops ◽  
Many Body ◽  
Quantum Numbers ◽  
The Many ◽  
Chern Simons

There is a topological connection between the boundary excitations of a quantum Hall fluid and the quantum numbers of its vortex-like bulk quasi-particles. I use this connection to examine the group properties of vortex excitations in a generalized quantum Hall fluid, and show how the vortex trajectories become Wilson lines interacting via Chern-Simons fields. As a result, I argue that non-abelian statistics, if they exist, should be independent of the detailed properties of the many-body wavefunction and will depend only on the bulk Hall conductivity tensor.

FLUID DYNAMICS, CHERN-SIMONS THEORY, AND THE QUANTUM HALL EFFECT

1991 ◽  
Vol 05 (16n17) ◽  
pp. 2735-2749 ◽  
Author(s):  
SAFI BAHCALL ◽  
LEONARD SUSSKIND
Keyword(s):  
Magnetic Field ◽  
Fluid Dynamics ◽  
Gauge Theory ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Simons Theory ◽  
Quantum Hall System ◽  
Chern Simons ◽  
Chern Simons Theory

In this paper we show that classical fluid dynamics in a plane is a gauge theory useful for studying aspects of the quantum Hall system. When the fluid is charged and placed in a magnetic field, Chern-Simons fields appear naturally and the fractional statistics of vortex excitations can be understood qualitatively. Applying the fluid picture to a gas of anyons shows that it superconducts.

scholarly journals Current Percolation in Medium with Boundaries under Quantum Hall Effect Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-6 ◽  
Author(s):  
M. U. Malakeeva ◽  
V. E. Arkhincheev
Keyword(s):  
Finite Number ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Hall Current ◽  
Quantum Hall ◽  
Singular Points ◽  
Hall Conductivity

The current percolation has been considered in the medium with boundaries under quantum Hall effect conditions. It has been shown that in that case the effective Hall conductivity has a nonzero value due to percolation of the Hall current through the finite number of singular points (in our model these are corners at the phase joints).

scholarly journals DUALITY IN SUPERSYMMETRIC YANG–MILLS AND THE QUANTUM HALL EFFECT

2006 ◽  
Vol 21 (20) ◽  
pp. 1567-1585
Author(s):  
BRIAN P. DOLAN
Keyword(s):  
Gauge Theory ◽  
Hall Effect ◽  
Experimental Evidence ◽  
Quantum Hall Effect ◽  
Modular Group ◽  
Quantum Hall ◽  
Low Energy ◽  
Kinetic Term ◽  
Yang Mills ◽  
Topological Parameter

The evidence for the parallel rôles played by the modular group in [Formula: see text] supersymmetric Yang–Mills in (3+1) dimensions and the quantum Hall effect in (2+1) dimensions is reviewed. In both cases a subgroup of the full modular group acts as a map between different low energy phases of the theory, parametrised by a complex parameter in the upper-half-complex plane whose real part is a topological parameter and whose imaginary part is the coupling associated the kinetic term of the effective U(1) gauge theory. In the case of the quantum Hall effect experimental evidence in favour of the modular action is also reviewed.

scholarly journals HIERARCHICAL WAVE FUNCTIONS OF FRACTIONAL QUANTUM HALL EFFECT ON THE TORUS

1993 ◽  
Vol 07 (14) ◽  
pp. 2655-2665 ◽  
Author(s):  
DINGPING LI
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Wave Functions ◽  
Simons Theory ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Chern Simons ◽  
Chern Simons Theory

One kind of hierarchical wave functions of Fractional Quantum Hall Effect on the torus is constructed. We find that the wave functions are closely related to the wave functions of generalized Abelian Chern-Simons theory.

W∞gauge theory and the quantum Hall effect

1995 ◽  
Vol 52 (4) ◽  
pp. 2747-2753 ◽  
Author(s):  
K. Shizuya
Keyword(s):  
Gauge Theory ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall
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