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

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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.

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References

  1. D.V. Ahluwalia, D. Grumiller, JCAP 07, 012 (2005).

    Article  ADS  Google Scholar 

  2. D.V. Ahluwalia, D. Grumiller, Phys. Rev. D 72, 067701 (2005).

    Article  ADS  Google Scholar 

  3. A.G. Cohen, S.L. Glashow, Phys. Rev. Lett. 97, 021601 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  4. D.V. Ahluwalia, S.P. Horvath, JHEP 11, 078 (2010).

    Article  ADS  Google Scholar 

  5. A.E. Bernardini, R. da Rocha, Phys. Lett. B 717, 238 (2012).

    Article  ADS  Google Scholar 

  6. M. Dias, F. de Campos, J.M. Hoff da Silva, Phys. Lett. B 706, 352 (2012).

    Article  ADS  Google Scholar 

  7. R. da Rocha, A.E. Bernardini, J.M. Hoff da Silva, JHEP 04, 110 (2011).

    Article  ADS  Google Scholar 

  8. J.M. Hoff da Silva, S.H. Pereira, JCAP 03, 009 (2014).

    Article  ADS  MathSciNet  Google Scholar 

  9. A. Basak, J.R. Bhatt, S. Shankaranarayanan, K.V. Prasantha Varma, JCAP 04, 025 (2013).

    Article  ADS  MathSciNet  Google Scholar 

  10. S. Kouwn, J. Lee, T.H. Lee, P. Oh, Mod. Phys. Lett. A 28, 1350121 (2013).

    Article  ADS  MathSciNet  Google Scholar 

  11. C.G. Boehmer, J. Burnett, D.F. Mota, D.J. Shaw, JHEP 07, 053 (2010).

    Article  ADS  Google Scholar 

  12. P. Lounesto, Clifford Algebras and Spinors (Cambridge University Press, Cambridge, 2002).

  13. H.M. Sadjadi, Gen. Relativ. Gravit. 44, 2329 (2012).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  14. Y.-X. Liu, X.-N. Zhou, K. Yang, F.-W. Chen, Phys. Rev. D 86, 064012 (2012).

    Article  ADS  Google Scholar 

  15. R. da Rocha, J.G. Pereira, Int. J. Mod. Phys. D 16, 1653 (2007).

    Article  ADS  MATH  Google Scholar 

  16. R. da Rocha, J.M. Hoff da Silva, J. Math. Phys. 48, 123517 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  17. C.G. Boehmer, Ann. Phys. 16, 38 (2007).

    Article  MATH  MathSciNet  Google Scholar 

  18. S. Vignolo, L. Fabbri, R. Cianci, J. Math. Phys. 52, 112502 (2011).

    Article  ADS  MathSciNet  Google Scholar 

  19. L. Fabbri, J. Math. Phys. 54, 062501 (2013).

    Article  ADS  MathSciNet  Google Scholar 

  20. D.V. Ahluwalia, C.-Y. Lee, D. Schritt, Phys. Rev. D 83, 065017 (2011).

    Article  ADS  Google Scholar 

  21. D.V. Ahluwalia, C.-Y. Lee, D. Schritt, T.F. Watson, Phys. Lett. B 687, 248 (2010).

    Article  ADS  Google Scholar 

  22. L.D. Sperança, Int. J. Mod. Phys. D 23, 1444003 (2014).

    Article  Google Scholar 

  23. K.E. Wunderle, R. Dick, Can. J. Phys. 87, 909 (2009).

    Article  ADS  Google Scholar 

  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. L. Fabbri, Phys. Rev. D 85, 047502 (2012).

    Article  ADS  Google Scholar 

  26. R. da Rocha, L. Fabbri, J.M. Hoff da Silva, R.T. Cavalcanti, J.A. Silva-Neto, J. Math. Phys. 54, 102505 (2013).

    Article  ADS  MathSciNet  Google Scholar 

  27. R. da Rocha, J.M. Hoff da Silva, EPL 107, 50001 (2014).

    Article  Google Scholar 

  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. R.J. Duffin, Phys. Rev. 54, 1114 (1938).

    Article  ADS  Google Scholar 

  30. N. Kemmer, Proc. R. Soc. London A 173, 91 (1939).

    Article  ADS  MathSciNet  Google Scholar 

  31. G. Petiau, University of Paris thesis, Académie Royale De Belgique, Classe Des Sciences. Mémoires, Collection 16 (1936) p. 1114.

  32. Harish-Chandra, Proc. R. Soc. London A 186, 502 (1946).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  33. R. Casana, V.Ya. Fainberg, J.T. Lunardi, B.M. Pimentel, R.G. Teixeira, Class. Quantum Grav. 20, 2457 (2003).

    Article  ADS  MATH  Google Scholar 

  34. H. Umezawa, Quantum Field Theory (North-Holland, Michigan, 1956).

  35. L.B. Castro, A.S. de Castro, Phys. Rev. A 90, 022101 (2014).

    Article  ADS  Google Scholar 

  36. V.Y. Fainberg, B.M. Pimentel, Theor. Math. Phys. 124, 1234 (2000).

    Article  MATH  MathSciNet  Google Scholar 

  37. R.A. Krajcik, M.M. Nieto, Am. J. Phys. 45, 818 (1977).

    Article  ADS  Google Scholar 

  38. E. Fischbach, J.D. Louck, M.M. Nieto, C.K. Scott, J. Math. Phys. 15, 60 (1974).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  39. Y. Nedjadi, R.C. Barrett, J. Math. Phys. 35, 4517 (1994).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  40. Y. Nedjadi, R.C. Barrett, J. Phys. A 27, 4301 (1994).

    Article  ADS  MATH  MathSciNet  Google Scholar 

  41. P.K. Jena, P.C. Naik, T. Pradhan, J. Phys. A 13, 2975 (1980).

    Article  ADS  MathSciNet  Google Scholar 

  42. N. Jacobson, Structure and Representations of Jordan Algebras (American Mathematical Society, Providence, 1968).

  43. A. Micali, M. Rachidi, Adv. Appl. Clifford Algebras 18, 875 (2008).

    Article  MATH  MathSciNet  Google Scholar 

  44. J. Alfaro, V.O. Rivelles, Phys. Lett. B 734, 239 (2014).

    Article  ADS  MathSciNet  Google Scholar 

  45. R.T. Cavalcanti, Int. J. Mod. Phys. D 23, 1444002 (2014).

    Article  Google Scholar 

  46. E.M. Corson, Introduction to Tensors, Spinors and Relativistic Waves (Blackie Son, London, 1953).

  47. W.I. Fushchich, A.G. Nikitin, Symmetries of Equations of Quantum Mechanics (Allerton Press Inc., New York, 1994).

  48. J.A. Nieto, Rev. Mex. Fis. 60, 371 (2014).

    Google Scholar 

  49. T.R. Cardoso, L.B. Castro, A.S. de Castro, J. Phys. A 45, 075302 (2012).

    Article  ADS  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Centro de Ciências Naturais e Humanas, UFABC, 09210-580, Santo André - SP, Brazil

    R. T. Cavalcanti

  2. Campus de Guaratinguetá - DFQ, UNESP, Av. Dr. Ariberto Pereira da Cunha, 333, 12516-410, Guaratinguetá - SP, Brazil

    J. M. Hoff da Silva

  3. Centro de Matemática, Computação e Cognição, UFABC, 09210-180, Santo André - SP, Brazil

    Roldão da Rocha

  4. International School for Advanced Studies (SISSA), Via Bonomea 265, 34136, Trieste, Italy

    Roldão da Rocha

Authors
  1. R. T. Cavalcanti
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  2. J. M. Hoff da Silva
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  3. Roldão da Rocha
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Correspondence to R. T. Cavalcanti.

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Cavalcanti, R.T., Hoff da Silva, J.M. & da Rocha, R. VSR symmetries in the DKP algebra: The interplay between Dirac and Elko spinor fields. Eur. Phys. J. Plus 129, 246 (2014). https://doi.org/10.1140/epjp/i2014-14246-4

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  • DOI: https://doi.org/10.1140/epjp/i2014-14246-4

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