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The European Physical Journal C

, Volume 56, Issue 4, pp 571–578 | Cite as

Gauge invariance and the CPT and Lorentz violating induced Chern–Simons-like term in extended QED

  • A. P. Baêta ScarpelliEmail author
  • Marcos Sampaio
  • M. C. Nemes
  • B. Hiller
Regular Article - Theoretical Physics

Abstract

The radiative induction of the CPT and Lorentz violating Chern–Simons (CS) term is reassessed. The massless and massive models are studied. Special attention is given to the preservation of gauge symmetry at higher orders in the background vector b μ when radiative corrections are considered. Both the study of the odd and even parity sectors of the complete vacuum polarization tensor at one-loop order and a non-perturbative analysis show that this symmetry must be preserved by quantum corrections. As a complement we obtain the result that transversality of the polarization tensor does not fix the value of the coefficient of the induced CS term.

PACS

11.30.Cp 11.30.Er 11.30.Qc 11.15.Bt 

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References

  1. 1.
    S.M. Carroll, G.B. Field, R. Jackiw, Phys. Rev. D 41, 1231 (1990) CrossRefADSGoogle Scholar
  2. 2.
    A.A. Andrianov, R. Soldati, Phys. Rev. D 51, 5961 (1995) CrossRefADSGoogle Scholar
  3. 3.
    M. Goldhaber, V. Trimble, J. Astrophys. Astron. 17, 17 (1996) CrossRefADSGoogle Scholar
  4. 4.
    D. Colladay, V.A. Kostelecký, Phys. Rev. D 55, 6760 (1997) CrossRefADSGoogle Scholar
  5. 5.
    S. Coleman, S.L. Glashow, Phys. Lett. B 405, 249 (1997) CrossRefADSGoogle Scholar
  6. 6.
    D. Colladay, V.A. Kostelecký, Phys. Rev. D 58, 116002 (1998) CrossRefADSGoogle Scholar
  7. 7.
    A.A. Andrianov, R. Soldati, Phys. Lett. B 435, 449 (1998) CrossRefADSGoogle Scholar
  8. 8.
    S. Coleman, S.L. Glashow, Phys. Rev. D 59, 116008 (1999) CrossRefADSGoogle Scholar
  9. 9.
    O. Bertolami, D.F. Mota, Phys. Lett. B 455, 96 (1999) CrossRefADSGoogle Scholar
  10. 10.
    C. Adam, F.R. Klinkhamer, Nucl. Phys. B 607, 247 (2001) zbMATHCrossRefADSGoogle Scholar
  11. 11.
    R. Jackiw, V.A. Kostelecký, Phys. Rev. Lett. 82, 3572 (1999) CrossRefADSGoogle Scholar
  12. 12.
    W.F. Chen, Phys. Rev. D 60, 085007 (1999) CrossRefADSGoogle Scholar
  13. 13.
    M. Pérez-Victoria, Phys. Rev. Lett. 83, 2518 (1999) CrossRefADSGoogle Scholar
  14. 14.
    J.-M. Chung, Phys. Lett. B 461, 138 (1999) CrossRefADSGoogle Scholar
  15. 15.
    W.F. Chen, G. Kunstatter, Phys. Rev. D 62, 105029 (2000) CrossRefADSGoogle Scholar
  16. 16.
    M. Chaichian, W.F. Chen, R. Gonzalez Felipe, Phys. Lett. B 503, 215 (2001) zbMATHCrossRefADSGoogle Scholar
  17. 17.
    B. Altschul, Phys. Rev. D 69, 125009 (2004) CrossRefADSGoogle Scholar
  18. 18.
    B. Altschul, Phys. Rev. D 70, 101701 (2004) CrossRefADSGoogle Scholar
  19. 19.
    B. Altschul, Phys. Rev. D 73, 0360055 (2006) MathSciNetGoogle Scholar
  20. 20.
    G. Bonneau, Nucl. Phys. B 593, 398 (2001) zbMATHCrossRefADSMathSciNetGoogle Scholar
  21. 21.
    G. Bonneau, L.C. Costa, J.L. Tomazelli, Int. J. Theor. Phys. 47, 1764 (2008) zbMATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    J.-M. Chung, Phys. Rev. D 60, 127901 (1999) CrossRefADSGoogle Scholar
  23. 23.
    J.-M. Chung, B.K. Chung, Phys. Rev. D 63, 105015 (2001) CrossRefADSGoogle Scholar
  24. 24.
    A.P. Baêta Scarpelli, M. Sampaio, M.C. Nemes, Phys. Rev. D 63, 046004 (2001) CrossRefADSGoogle Scholar
  25. 25.
    A.P. Baêta Scarpelli, M. Sampaio, B. Hiller, M.C. Nemes, Phys. Rev. D 64, 046013 (2001) CrossRefADSGoogle Scholar
  26. 26.
    O.A. Battistel, G. Dallabona, Nucl. Phys. B 610, 316 (2001) zbMATHCrossRefADSGoogle Scholar
  27. 27.
    M. Pérez-Victoria, J. High Energy Phys. 0104, 032 (2001) CrossRefGoogle Scholar
  28. 28.
    A.A. Andrianov, P. Giacconi, R. Soldati, J. High Energy Phys. 0202, 030 (2002) CrossRefADSGoogle Scholar
  29. 29.
    D. Ebert, V.Ch. Zhukovsky, A.S. Razumovsky, Phys. Rev. D 70, 025003 (2004) CrossRefADSGoogle Scholar
  30. 30.
    A.P. Baêta Scarpelli, H. Belich, J.L. Boldo, J.A. Helaÿel-Neto, Phys. Rev. D 67, 085021 (2003) CrossRefADSGoogle Scholar
  31. 31.
    H. Belich, J.L. Boldo, L.P. Colatto, J.A. Helayel-Neto, A.L.M.A. Nogueira, Phys. Rev. D 68, 065030 (2003) CrossRefADSGoogle Scholar
  32. 32.
    R. Lehnert, Phys. Rev. D 68, 085003 (2003) CrossRefADSMathSciNetGoogle Scholar
  33. 33.
    V.A. Kostelecký, R. Lehnert, M.J. Perry, Phys. Rev. D 68, 123511 (2003) CrossRefADSMathSciNetGoogle Scholar
  34. 34.
    O. Bertolami, R. Lehnert, R. Potting, A. Ribeiro, Phys. Rev. D 69, 083513 (2004) CrossRefADSGoogle Scholar
  35. 35.
    W.G. Ney, J.A. Helaÿel-Neto, W. Spalenza, hep-th/0502037
  36. 36.
    H. Belich, T. Costa-Soares, M.M. Ferreira Jr., J.A. Helaÿel-Neto, Eur. Phys. J. C 42, 127 (2005) CrossRefADSGoogle Scholar
  37. 37.
    H. Belich, T. Costa-Soares, M.M. Ferreira Jr., J.A. Helaÿel-Neto, Eur. Phys. J. C 41, 421 (2005) CrossRefADSGoogle Scholar
  38. 38.
    V.B. Bezerra, C.N. Ferreira, J.A. Helaÿel-Neto, Phys. Rev. D 71, 044018 (2005) CrossRefADSMathSciNetGoogle Scholar
  39. 39.
    A. Das, J. Gamboa, J. Lopez-Sarrion, F.A. Schaposnik, Phys. Rev. D 72, 107702 (2005) CrossRefADSMathSciNetGoogle Scholar
  40. 40.
    A.J. Hariton, R. Lehnert, Phys. Lett. A 367, 11 (2007) CrossRefADSMathSciNetGoogle Scholar
  41. 41.
    A.C. Lehum, A.F. Ferreira, M. Gomes, A.J. da Silva, Phys. Rev. D 76, 105021 (2007) CrossRefADSMathSciNetGoogle Scholar
  42. 42.
    M. Gomes, T. Mariz, J.R. Nascimento, A.J. da Silva, arXiv:0709.2904
  43. 43.
    A.F. Ferrari, M. Gomes, A.J. da Silva, J.R. Nascimento, E. Passos, A.Y. Petrov, Phys. Lett. B 652, 174 (2007) CrossRefADSMathSciNetGoogle Scholar
  44. 44.
    M.M. Ferreira Jr., A.R. Gomes, R.C.C. Lopes, Phys. Rev. D 76, 1055031 (2007) CrossRefGoogle Scholar
  45. 45.
    M.M. Ferreira Jr., A.R. Gomes, arXiv:0803.4010
  46. 46.
    R. Casana, M.M. Ferreira Jr., C.E.H. Santos, arXiv:0804.0431
  47. 47.
    O.A. Battistel, PhD thesis, Federal University of Minas Gerais, 2000 Google Scholar
  48. 48.
    O.A. Battistel, A.L. Mota, M.C. Nemes, Mod. Phys. Lett. A 13, 1597 (1998) CrossRefADSGoogle Scholar
  49. 49.
    M. Sampaio, A.P. Baêta Scarpelli, B. Hiller, A. Brizola, M.C. Nemes, S. Gobira, Phys. Rev. D 65, 125023 (2002) CrossRefADSGoogle Scholar
  50. 50.
    S.R. Gobira, M.C. Nemes, Int. J. Theor. Phys. 42, 2765 (2003) zbMATHCrossRefMathSciNetGoogle Scholar
  51. 51.
    D. Carneiro, A.P. Baêta Scarpelli, M. Sampaio, M.C. Nemes, J. High Energy Phys. 12, 044 (2003) CrossRefADSGoogle Scholar
  52. 52.
    M. Sampaio, A.P. Baêta Scarpelli, J.E. Ottoni, M.C. Nemes, Int. J. Theor. Phys. 45, 436 (2006) CrossRefGoogle Scholar
  53. 53.
    L.A.M. Souza, M. Sampaio, M.C. Nemes, Phys. Lett. B 632, 717 (2006) CrossRefADSMathSciNetGoogle Scholar
  54. 54.
    J.E. Ottoni, A.P.B. Scarpelli, M. Sampaio, M.C. Nemes, Phys. Lett. B 642, 253 (2006) CrossRefADSGoogle Scholar
  55. 55.
    E.W. Dias, B. Hiller, A.L. Mota, M.C. Nemes, M. Sampaio, A.A. Osipov, Mod. Phys. Lett. A 21, 339 (2006) zbMATHCrossRefADSGoogle Scholar
  56. 56.
    B. Hiller, A.L. Mota, M.C. Nemes, A.A. Osipov, M. Sampaio, Nucl. Phys. A 769, 53 (2006) CrossRefADSGoogle Scholar
  57. 57.
    O. Battistel, G. Dallabona, Eur. Phys. J. C 45, 721 (2006) CrossRefADSMathSciNetGoogle Scholar
  58. 58.
    C.R. Pontes, A.P. Baêta Scarpelli, M. Sampaio, M.C. Nemes, J. Phys. G: Nucl. Part. Phys. 34(10), 2215 (2007) CrossRefADSGoogle Scholar
  59. 59.
    C.R. Pontes, A.P. Baêta Scarpelli, M. Sampaio, J.L. Acebal, M.C. Nemes, Eur. Phys. J. C 53, 121 (2008) CrossRefADSGoogle Scholar
  60. 60.
    E.W. Dias, A.P. Baêta Scarpelli, L.C.T. Brito, M. Sampaio, M.C. Nemes, Eur. Phys. J. C 55, 667 (2008) CrossRefADSGoogle Scholar
  61. 61.
    K. Fujikawa, Phys. Rev. Lett. 42, 1195 (1979) CrossRefADSGoogle Scholar
  62. 62.
    G. ’t Hooft, Nucl. Phys. B 33, 173 (1971) CrossRefADSMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag / Società Italiana di Fisica 2008

Authors and Affiliations

  • A. P. Baêta Scarpelli
    • 1
    Email author
  • Marcos Sampaio
    • 2
  • M. C. Nemes
    • 2
  • B. Hiller
    • 3
  1. 1.Centro Federal de Educação Tecnológica, MGNova Gameleira Belo HorizonteBrazil
  2. 2.Physics Department, ICExFederal University of Minas GeraisBelo HorizonteBrazil
  3. 3.Departamento de FisicaUniversidade de CoimbraCoimbraPortugal

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