Sendic Estrada–Jiménez and Hugo García–Compeán
Departamento de Física Centro de Investigación y de Estudios Avanzados del IPN Apdo. Postal 14–740, 07000, México D.F., México
Recibido el 18 de julio de 2005
Aceptado el 14 de marzo de 2005
Abstract
]]> The fractional quantum Hall effect is studied in the context of the noncommutative quantum field theory in (2+1) dimensions. For the filling factor v = 1/2, the noncommutative effective field theory incorporates a Chern–Simons gauge field (in the temporal gauge) coupled to the matter in the presence of a suitable quenched external magnetic field. After providing the Feynman rules for this system, the noncommutative corrections to the self–energy of quasiparticles are computed, showing that it is zero at Hartree–Fock approximation. Finally, in this approach it is proved that the density ρ satisfies a noncommutative deformation of the w∞–algebra.
Keywords: Noncommutative field theory; fractional quantum Hall effect; Chern–Simons theory.
Resumen
El efecto Hall cuántico fraccionario se estudia en el contexto de la teoría cuántica de campos no conmutativa en (2+1) dimensiones. Para el factor de llenado v = 1/2, la teoría de campos efectiva incorpora un campo de norma de Chern–Simons (en la norma temporal) acoplado a la materia en la presencia de un campo magnético externo apropiadamente cancelado. Después de dar las reglas de Feynman para este sistema, las correcciones no conmutativas de la autoenegía de las cuasipartículas son calculadas y se muestra que son cero en la aproximación de Hartree–Fock. Finalmente, en este enfoque se prueba que la densidad ρ satisface una deformación no conmutativa del álgebra w∞.
Descriptores: Teoría de campos no conmutativa; efecto Hall cuántico fraccionario; teoría de Chern–Simons.
PACS: 11.10.Nx;73.43.Lp; 11.10.Gh
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Acknowledgments
This work was supported in part by a CONACyT México grant No. 33951E. The work of S.E.–J. is supported by a CONACyT graduate fellowship. S. Estrada–Jiménez whishes to thank Prof. Yong–Shi Wu for useful discussions and suggestions concerning the subject of this paper and for his kind hospitality at the University of Utah, where part of this work was outlined.
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