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CHIRAL ANOMALY IN EUCLIDEAN (2+1)-DIMENSIONAL SPACE AND AN APPLICATION TO THE QUANTUM HALL EFFECT

PAUL BRACKEN

Department of Mathematics, University of Texas, Edinburg, TX 78541-2999, USA

https://doi.org/10.1142/S0217979208039848Cited by:3 (Source: Crossref)

Abstract

The chiral anomaly in (2+1)-dimensions and its relationship to the zero mode of the Dirac equation in the massless case is studied. Solutions are obtained for the Dirac equation under a vector potential which generates a constant magnetic field. It is shown that there is an anomaly term associated with the corresponding chiral transformation. It can be calculated by using the regularization procedure of Fujikawa. The results are applied to the quantum Hall effect.

Keywords:

PACS: 73.43.-f, 02.30.Jr

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References

M. A. Shifman, Physics Reports 209, 341 (1991), DOI: 10.1016/0370-1573(91)90020-M. Crossref, Web of Science, ADS, Google Scholar
S. L. Adler and W. A. Bardeen, Phys. Rev. 182, 1517 (1969), DOI: 10.1103/PhysRev.182.1517. Crossref, Web of Science, ADS, Google Scholar
K. Ishikawa, Phys. Rev. Lett. 53, 1615 (1984), DOI: 10.1103/PhysRevLett.53.1615. Crossref, Web of Science, ADS, Google Scholar
K. Ishikawa, Phys. Rev. D 31, 1432 (1985), DOI: 10.1103/PhysRevD.31.1432. Crossref, Web of Science, ADS, Google Scholar
R. E. Prange and S. M. Girvin , The Quantum Hall Effect ( Springer Verlag , New York, USA , 1987 ) . Crossref, Google Scholar
K. von Klitzing, G. Dorda and M. Pepper, Phys. Rev. Lett. 45, 494 (1980), DOI: 10.1103/PhysRevLett.45.494. Crossref, Web of Science, Google Scholar
P. Bracken, Canadian J. of Phys. 79, 1121 (2001), DOI: 10.1139/cjp-79-9-1121. Crossref, Web of Science, ADS, Google Scholar
P. Bracken, Int. J. Mod. Phys. E 13, 801 (2004), DOI: 10.1142/S0218301304002417. Link, ADS, Google Scholar
J. K. Jain and R. K. Kamilla , Composite Fermions , ed. O. Heinonen ( World Scientific , Singapore , 2003 ) . Google Scholar
G. Esposito , G. Marmo and G. Sudarshan , From Classical to Quantum Mechanics ( Cambridge , England , 2004 ) . Crossref, Google Scholar
K. Fujikawa, Phys. Rev. D 21, 2848 (1980), DOI: 10.1103/PhysRevD.21.2848. Crossref, Web of Science, Google Scholar
K. Fujikawa, Phys. Rev. D 31, 341 (1985), DOI: 10.1103/PhysRevD.31.341. Crossref, Web of Science, ADS, Google Scholar
A. Das , Field Theory, A Path Integral Approach 75 ( World Scientific , Singapore , 2006 ) . Crossref, Google Scholar
W. Dittrich and M. Reuter , Selected Topics in Gauge Theories , Lecture Notes in Physics 244 ( Springer-Verlag , Berlin , 1986 ) . Google Scholar