VSR symmetries in the DKP algebra: The interplay between Dirac and Elko spinor fields

  • R. T. Cavalcanti
  • J. M. Hoff da Silva
  • Roldão da Rocha
Regular Article

Abstract

VSR symmetries are here naturally incorporated in the DKP algebra on the spin-0 and the spin-1 DKP sectors. We show that the Elko (dark) spinor fields structure plays an essential role in accomplishing this aim, unravelling hidden symmetries on the bosonic DKP fields under the action of discrete symmetries.

Keywords

Dark Matter Tensor Product Discrete Symmetry Minkowski Spacetime Dirac Spinor 

References

  1. 1.
    D.V. Ahluwalia, D. Grumiller, JCAP 07, 012 (2005).ADSCrossRefGoogle Scholar
  2. 2.
    D.V. Ahluwalia, D. Grumiller, Phys. Rev. D 72, 067701 (2005).ADSCrossRefGoogle Scholar
  3. 3.
    A.G. Cohen, S.L. Glashow, Phys. Rev. Lett. 97, 021601 (2006).ADSCrossRefMathSciNetGoogle Scholar
  4. 4.
    D.V. Ahluwalia, S.P. Horvath, JHEP 11, 078 (2010).ADSCrossRefGoogle Scholar
  5. 5.
    A.E. Bernardini, R. da Rocha, Phys. Lett. B 717, 238 (2012).ADSCrossRefGoogle Scholar
  6. 6.
    M. Dias, F. de Campos, J.M. Hoff da Silva, Phys. Lett. B 706, 352 (2012).ADSCrossRefGoogle Scholar
  7. 7.
    R. da Rocha, A.E. Bernardini, J.M. Hoff da Silva, JHEP 04, 110 (2011).ADSCrossRefGoogle Scholar
  8. 8.
    J.M. Hoff da Silva, S.H. Pereira, JCAP 03, 009 (2014).ADSCrossRefMathSciNetGoogle Scholar
  9. 9.
    A. Basak, J.R. Bhatt, S. Shankaranarayanan, K.V. Prasantha Varma, JCAP 04, 025 (2013).ADSCrossRefMathSciNetGoogle Scholar
  10. 10.
    S. Kouwn, J. Lee, T.H. Lee, P. Oh, Mod. Phys. Lett. A 28, 1350121 (2013).ADSCrossRefMathSciNetGoogle Scholar
  11. 11.
    C.G. Boehmer, J. Burnett, D.F. Mota, D.J. Shaw, JHEP 07, 053 (2010).ADSCrossRefGoogle Scholar
  12. 12.
    P. Lounesto, Clifford Algebras and Spinors (Cambridge University Press, Cambridge, 2002).Google Scholar
  13. 13.
    H.M. Sadjadi, Gen. Relativ. Gravit. 44, 2329 (2012).ADSCrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    Y.-X. Liu, X.-N. Zhou, K. Yang, F.-W. Chen, Phys. Rev. D 86, 064012 (2012).ADSCrossRefGoogle Scholar
  15. 15.
    R. da Rocha, J.G. Pereira, Int. J. Mod. Phys. D 16, 1653 (2007).ADSCrossRefMATHGoogle Scholar
  16. 16.
    R. da Rocha, J.M. Hoff da Silva, J. Math. Phys. 48, 123517 (2007).ADSCrossRefMathSciNetGoogle Scholar
  17. 17.
    C.G. Boehmer, Ann. Phys. 16, 38 (2007).CrossRefMATHMathSciNetGoogle Scholar
  18. 18.
    S. Vignolo, L. Fabbri, R. Cianci, J. Math. Phys. 52, 112502 (2011).ADSCrossRefMathSciNetGoogle Scholar
  19. 19.
    L. Fabbri, J. Math. Phys. 54, 062501 (2013).ADSCrossRefMathSciNetGoogle Scholar
  20. 20.
    D.V. Ahluwalia, C.-Y. Lee, D. Schritt, Phys. Rev. D 83, 065017 (2011).ADSCrossRefGoogle Scholar
  21. 21.
    D.V. Ahluwalia, C.-Y. Lee, D. Schritt, T.F. Watson, Phys. Lett. B 687, 248 (2010).ADSCrossRefGoogle Scholar
  22. 22.
    L.D. Sperança, Int. J. Mod. Phys. D 23, 1444003 (2014).CrossRefGoogle Scholar
  23. 23.
    K.E. Wunderle, R. Dick, Can. J. Phys. 87, 909 (2009).ADSCrossRefGoogle Scholar
  24. 24.
    A. Alves, F. de Campos, M. Dias, J.M. Hoff da Silva, Searching for Elko dark matter spinors at the CERN LHC, arXiv:1401.1127 [hep-ph].
  25. 25.
    L. Fabbri, Phys. Rev. D 85, 047502 (2012).ADSCrossRefGoogle Scholar
  26. 26.
    R. da Rocha, L. Fabbri, J.M. Hoff da Silva, R.T. Cavalcanti, J.A. Silva-Neto, J. Math. Phys. 54, 102505 (2013).ADSCrossRefMathSciNetGoogle Scholar
  27. 27.
    R. da Rocha, J.M. Hoff da Silva, EPL 107, 50001 (2014).CrossRefGoogle Scholar
  28. 28.
    D.V. Ahluwalia, On a local mass dimension one Fermi field of spin one-half and the theoretical crevice that allows it, arXiv:1305.7509 [hep-th].
  29. 29.
    R.J. Duffin, Phys. Rev. 54, 1114 (1938).ADSCrossRefGoogle Scholar
  30. 30.
    N. Kemmer, Proc. R. Soc. London A 173, 91 (1939).ADSCrossRefMathSciNetGoogle Scholar
  31. 31.
    G. Petiau, University of Paris thesis, Académie Royale De Belgique, Classe Des Sciences. Mémoires, Collection 16 (1936) p. 1114.Google Scholar
  32. 32.
    Harish-Chandra, Proc. R. Soc. London A 186, 502 (1946).ADSCrossRefMATHMathSciNetGoogle Scholar
  33. 33.
    R. Casana, V.Ya. Fainberg, J.T. Lunardi, B.M. Pimentel, R.G. Teixeira, Class. Quantum Grav. 20, 2457 (2003).ADSCrossRefMATHGoogle Scholar
  34. 34.
    H. Umezawa, Quantum Field Theory (North-Holland, Michigan, 1956).Google Scholar
  35. 35.
    L.B. Castro, A.S. de Castro, Phys. Rev. A 90, 022101 (2014).ADSCrossRefGoogle Scholar
  36. 36.
    V.Y. Fainberg, B.M. Pimentel, Theor. Math. Phys. 124, 1234 (2000).CrossRefMATHMathSciNetGoogle Scholar
  37. 37.
    R.A. Krajcik, M.M. Nieto, Am. J. Phys. 45, 818 (1977).ADSCrossRefGoogle Scholar
  38. 38.
    E. Fischbach, J.D. Louck, M.M. Nieto, C.K. Scott, J. Math. Phys. 15, 60 (1974).ADSCrossRefMATHMathSciNetGoogle Scholar
  39. 39.
    Y. Nedjadi, R.C. Barrett, J. Math. Phys. 35, 4517 (1994).ADSCrossRefMATHMathSciNetGoogle Scholar
  40. 40.
    Y. Nedjadi, R.C. Barrett, J. Phys. A 27, 4301 (1994).ADSCrossRefMATHMathSciNetGoogle Scholar
  41. 41.
    P.K. Jena, P.C. Naik, T. Pradhan, J. Phys. A 13, 2975 (1980).ADSCrossRefMathSciNetGoogle Scholar
  42. 42.
    N. Jacobson, Structure and Representations of Jordan Algebras (American Mathematical Society, Providence, 1968).Google Scholar
  43. 43.
    A. Micali, M. Rachidi, Adv. Appl. Clifford Algebras 18, 875 (2008).CrossRefMATHMathSciNetGoogle Scholar
  44. 44.
    J. Alfaro, V.O. Rivelles, Phys. Lett. B 734, 239 (2014).ADSCrossRefMathSciNetGoogle Scholar
  45. 45.
    R.T. Cavalcanti, Int. J. Mod. Phys. D 23, 1444002 (2014).CrossRefGoogle Scholar
  46. 46.
    E.M. Corson, Introduction to Tensors, Spinors and Relativistic Waves (Blackie Son, London, 1953).Google Scholar
  47. 47.
    W.I. Fushchich, A.G. Nikitin, Symmetries of Equations of Quantum Mechanics (Allerton Press Inc., New York, 1994).Google Scholar
  48. 48.
    J.A. Nieto, Rev. Mex. Fis. 60, 371 (2014).Google Scholar
  49. 49.
    T.R. Cardoso, L.B. Castro, A.S. de Castro, J. Phys. A 45, 075302 (2012).ADSCrossRefMathSciNetGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • R. T. Cavalcanti
    • 1
  • J. M. Hoff da Silva
    • 2
  • Roldão da Rocha
    • 3
    • 4
  1. 1.Centro de Ciências Naturais e HumanasUFABCSanto André - SPBrazil
  2. 2.Campus de Guaratinguetá - DFQUNESPGuaratinguetá - SPBrazil
  3. 3.Centro de Matemática, Computação e CogniçãoUFABCSanto André - SPBrazil
  4. 4.International School for Advanced Studies (SISSA)TriesteItaly

Personalised recommendations