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

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.

U(1) gauge theory of the quantum hall effect

1991 ◽  
Vol 21 (11) ◽  
pp. 1329-1333 ◽  
Author(s):  
C. Dariescu ◽  
Marina Dariescu
Keyword(s):  
Gauge Theory ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall

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.

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.

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