Electron Monopole Duality in Quantum Hall Effect
Pawan Ku. Joshi, Praveen Singh Bisht, Om Prakash Singh Negi
DOI: 10.4236/jemaa.2011.31004   PDF    HTML     6,136 Downloads   10,218 Views   Citations


Starting from the duality between electric and magnetic field, we have made an attempt to discuss the quantum hall effect from the consideration of magnetic monopole in view of electron monopole duality. Starting from the dual dy-namics of electric and magnetic charges, we have reformulated a consistent theory of quantum hall effect in presence of monopole. Speculating the existence of magnetic monopoles in magnetic materials (metals), we have accordingly modi-fied the parameters; like drift velocity, current density, Hamiltonian and eigen values and eigen function for harmonic oscillator; resposible to examine the quantum Hall effect in metals.

Share and Cite:

P. Joshi, P. Bisht and O. Negi, "Electron Monopole Duality in Quantum Hall Effect," Journal of Electromagnetic Analysis and Applications, Vol. 3 No. 1, 2011, pp. 22-26. doi: 10.4236/jemaa.2011.31004.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] E. H. Hall, “On a New Action of the Magnet on Electric Currents,” American Journal of Mathematics, Vol. 2, 1879, pp. 287-292.
[2] K. Von Klitzing, G. Dorda and M. Pepper, “New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall,” Physical Review Letters, Vol. 45, No. 6, 1980, pp. 494-497.
[3] R. B. Laughlin, “Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations,” In: R. E. Prange and S. M. Girvin, Eds., Physical Review Letters, Vol. 50, No. 18, 1983, pp. 1395-1398.
[4] P. A. M. Dirac, “Quantised Singularities in the Electromagnetic Field,” Proceedings of Royal Society, London, 1931, pp. 60-72.
[5] P. B. Price, E. K. Shirk, W. Z. Osborne and L. S. Pinsky, “Evidence for Detection of a Moving Magnetic Monopole,” Physical Review Letters, Vol. 35, No. 8, 1975, pp. 487-490.
[6] S. Zhang et al, “A Four-Dimensional Generalization of the Quantum Hall Effect,” Science, Vol. 294, No. 5543, 2001, pp. 823-828.
[7] S. Sondhi, “An Experiment Based on Wien’s Theory of Electrolytes Has Now Measured Its Value,” Nature, Vol. 461, No. 7266, 2009, pp. 888-889.
[8] N. Seiberg and E. Witten, “Monopole Condensation, And Confinement in N=2 Supersymmetric Yang-Mills Theory,” Nuclear Physics, Vol. 426, No. 1, 1994, pp. 19-52.
[9] M. E. Peskin, “Dualities in Supersymmetric Yang-Mills Theories,” hep-th/9703136.
[10] P. S. Bisht and O. P. S. Negi, “Revisiting Quaternionic Dual Electrodynamics,” International Journal of Theoretical Physics, Vol. 47, No. 12, 2008, pp. 3108-3120.
[11] J. E. Avron, D. Osadchy and R. Seiler, “Topological Look at the Quantum Hall Effect,” Physics Today, Vol. 56, No. 8, August 2003, p. 38.
[12] G. t’ Hooft, “Magnetic, Monopoles in Unified Gauge Theories,” Nuclear Physics B, Vol. 79, No. 2, 1974, pp. 276-284.

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.