Abstract
We propose a modification of standard linear electrodynamics in four dimensions, where effective non-trivial interactions of the electromagnetic field with itself and with matter fields induce Lorentz violating Chern–Simons terms. This yields two consequences: it provides a more realistic and general scenario for the breakdown of Lorentz symmetry in electromagnetism and it may explain the effective behavior of the electromagnetic field in certain planar phenomena (for instance, Hall effect). A number of proposals for non-linear electrodynamics is discussed along the paper. Important physical implications of the breaking of Lorentz symmetry, such as optical birefringence and the possibility of having conductance in the vacuum are commented on.
Similar content being viewed by others
References
The most important original paper is S. Deser, R. Jackiw, S. Templeton, Ann. Phys. 140, 372 (1982), [Erratum-ibid. 185, 406 (1988)], reprinted in ibid. 281, 409 (2000). More recent and introductory articles are G.V. Dunne, http://arXiv.org/abs/hep-th/9902115; R. Jackiw, MIT-CTP-1824 DIAS Working Seminar, Dublin, Ireland, May 1989: 19th GIFT School, Jaca, Spain, June 1989: 8th Symp., Mt. Sorak, Korea, July 1989: Banff Summer School, August 1989: 29th Schladming School, Schladming, Austria, March 1990. (refs de Chern simons en 3 dim eletrodinamica)
W.A. Moura-Melo, J.A. Helayël-Neto, Phys. Rev. D 63, 065013 (2001); hep-th/0004143; W.A. Moura-Melo, Peculiar Aspects of Planar Maxwell and Maxwell–Chern–Simons Electrodynamics, Ph.D. Thesis, CBPF (2001) (avaiable at http://www.cbpf.br/∼dcp/papers/)
S.C. Zhang, T.H. Hansson, S. Kivelson, Phys. Rev. Lett. 62, 82 (1988)
A. Lopez, E. Fradkin, Phys. Rev. B 44, 5246 (1991)
R.E. Prange, S.M. Girvin (Eds.), The Quantum Hall Effect, 2nd. ed. (Springer-Verlag, New York 1990); S. Das Sarma, A. Pinczuk (Eds.), Perspectives in Quantum Hall Effects (Wiley, New York 1997); O. Heinonen (Ed.), Composite Fermions (World Scientific, Singapore 1998) (CS y FQHE)
S.M. Carroll, G.B. Field, R. Jackiw, Phys. Rev. D 41, 1231 (1990)
C. Adam, F.R. Klinkhamer, Nucl. Phys. B 607, 247 (2001); Phys. Lett. B 513, 245 (2001); A. Kostelecky, R. Lehnert, Phys. Rev. D 63, 065008 (2001); A.A. Andrianov, R. Soldati, L. Sorbo, Phys. Rev. D 59, 025002 (1999); R. Jackiw, A. Kostelecky, Phys. Rev. Lett. 82, 3572 (1999); J.-M. Chung, B.K. Chung, Phys. Rev. D 63, 105015 (2001); J.-M. Chung , Phys. Rev. D 60, 127901 (1999); M. Perez-Victoria, Phys. Rev. Lett. 83, 2518 (1999); G. Bonneau, Nucl. Phys. B 593, 398 (2001); M. Perez-Victoria, JHEP 0104, 032 (2001)
H. Belich, M.M. Ferreira Jr., J.A. Helayël-Neto, M.T.D. Orlando Phys. Rev. D 67, 125011 (2003) (hep-th/0212330); H. Belich, M.M. Ferreira Jr., J.A. Helayël-Neto, M.T.D. Orlando, Phys. Rev. D 68, 025005 (2003) (hep-th/0301224); H. Belich, M.M. Ferreira Jr., J.A. Helayel-Neto, Nucl. Phys. Proc. Suppl. 127, 105 (2004) (hep-th/0305089); M.M. Ferreira, Phys. Rev. D 70, 045013 (2004)
R.C. Paschoal, J.A. Helayel-Neto, L.P.G. de Assis, CBPF-NF-018-04, hep-th/0407109; R.C. Paschoal, J.A. Helayel-Neto, Phys. Lett. A 313, 412 (2003)
F.R. Klinkhamer, NPB 578, 277 (2000), hep-th/9912169
J. Stern, Phys. Lett. B 265, 119 (1991); I.I. Kogan, Phys. Lett. B 262, 83 (1991); S.M. Latinsky, D.P. Sorokin, JETP Lett. 53, 187 (1991); Mod. Phys. Lett. A 6, 3525 (1991), and references therein; H. Belich, T. Costa-Soares, M.M. Ferreira Jr., J.A. Helayel-Neto, M.T.D. Orlando, Gauge Theories with Lorentz-symmetry Violation and Electrically Charged Vortices in the Planar Regime (hep-th/0407260); S. Ghosh, Pauli Term, Anyons, “Cooper Pair”, ... or Noncommutative Maxwell–Chern–Simons, hep-th/0407086
S.M. Carroll, G. B. Field, Phys. Rev. Lett. 79, 2394 (1997); J.W. Moffat, Int. J. Mod. Phys. D 12, 1279 (2003); E.O. Iltan, Mod. Phys. Lett. A 19, 327 (2004); S. Coleman, S.L. Glashow, Phys. Rev. D 59, 116008 (1999)
M. Goldhaber, V. Trimble, J. Astrophys. Astron. 17, 17 (1996); V.B. Bezerra, H.J. Mosquera Cuesta, C.N. Ferreira, Phys. Rev. D 67, 084011 (2003)
V. Alan Kostelecky, S. Samuel, Phys. Rev. D 39, 683 (1989)
L.P. Colatto, A.L.A. Penna, W.C. Santos, Eur. Phys. J. C 36, 79 (2004) (hep-th/0310220)
R.B. Loughlin, Phys. Rev. Lett. 50, 1395 (1983)
J. Jain, Phys. Rev. Lett. 63, 199 (1989)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Botta Cantcheff, M. Lorentz symmetry breaking and planar effects from non-linear electrodynamics. Eur. Phys. J. C 46, 247–254 (2006). https://doi.org/10.1140/epjc/s2006-02483-0
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjc/s2006-02483-0