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The Explicit Relation Between the DKP Equation and the Klein-Gordon Equation

Year 2019, Volume: 1 Issue: 2, 69 - 76, 29.12.2019

Abstract

DKP equation describes spin-0 and spin-1 relativistic particles. Many researchers have been interested in the DKP equation. In this work, we give an explicit relation between the DKP and the KG equations for both the spin-0 particle in (1+3) dimensions and spin-1 particle in (1+1) dimensions. From the DKP equation in its explicit form, we get another system generated by the KG equation, which gives us the equivalence between the DKP equation and the KG equation. Using this equivalence, the Volkov-like solution of the DKP equation for the spin-0 particle in the field of an electromagnetic plane wave, is calculated.





Supporting Institution

This paper is the full-length paper of my communication at the third international conference of mathematical sciences (ICMS 2019).

References

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  • [3] N. Kemmer, The particle aspect of meson theory, Proc. R. Soc. A 173(952) (1939) 91-116.
  • [4] E. Fischbach, M.M. Nieto, and C.K. Scott, The Association of the Sakata-Taketani (Feshbach-Villars) Field with the Kemmer Field, under Symmetry Breaking, Prog. Theor. Phys. 48(2) (1972) 574-595.
  • [5] R.A. Krajcik, and M.M. Nieto, Bhabha first-order wave equations: I. C, P, and T, Phys. Rev. D 10(12) (1974) 4049-4063.
  • [6] Y. Nedjadi, and R.C. Barrett, On the properties of the Duffin-Kemmer-Petiau equation, J. Phys. G: Nucl. Part. Phys. 19 (1993) 87-98.
  • [7] V.Ya. Fainberg, and B.M. Pimentel, On equivalence of Duffin-Kemmer-Petiau and Klein- Gordon equations, B. J. Phys. 30(2) (2000) 275-281.
  • [8] J.T. Lunardi, B.M. Pimentel, R.G. Teixeira, and J.S. Valverde, Remarks on Duffin-Kemmer- Petiau theory and gauge invariance, Phys. Lett. A 268(3) (2000) 165-173.
  • [9] L. Chetouani, M. Merad, T. Boudjedaa, and A. Lecheheb, Solution of Duffin-Kemmer-Petiau equation for the step potential, Int. J. Theor. Phys. 43(4) (2004) 1147-1159.
  • [10] M. Merad, DKP equation with smooth potential and position-dependent mass, Int. J. Theor. Phys. 46(8) (2007) 2105-2118.
  • [11] B. Boutabia-Ch ́eraitia, and T. Boudjedaa, The Green function for the Duffin-Kemmer- Petiau equation, J. Geom. Phys. 62(10) (2012) 2038-2043.
  • [12] J.T. Lunardi, A note on the Duffin-Kemmer-Petiau equation in (1 + 1) space-time dimen- sions, J. Math. Phys. 58 (2017) 123501.
  • [13] V.B. Berestetskii, E.M. Lifshitz, and L.P. Pitaevskii, Quantum electrodynamics, Pergamon Press Ltd., Headingt.on Hill Hall, Oxford OX3 OBW, England. Vol 4. 2nd ed (1982).
  • [14] D. Bouchefra, and B. Boudjedaa, The explicit relation between the DKP equation and the Klein-Gordon equation, to appear in AIP Conference Proceedings of Third International Conference of Mathematical Sciences (ICMS 2019).
Year 2019, Volume: 1 Issue: 2, 69 - 76, 29.12.2019

Abstract

References

  • [1] G. Petiau, Contribution `a la th ́eorie des ́equations d’ondes corpusculaires, Ph.D. thesis, University of Paris, 1936. Published in Acad. Roy. de Belg., Classe Sci., Mem in 8◦ 16(2) (1936).
  • [2] R.J. Duffin, On the characteristic matrices of covariant systems, Phys. Rev. 54 (1938) 1114.
  • [3] N. Kemmer, The particle aspect of meson theory, Proc. R. Soc. A 173(952) (1939) 91-116.
  • [4] E. Fischbach, M.M. Nieto, and C.K. Scott, The Association of the Sakata-Taketani (Feshbach-Villars) Field with the Kemmer Field, under Symmetry Breaking, Prog. Theor. Phys. 48(2) (1972) 574-595.
  • [5] R.A. Krajcik, and M.M. Nieto, Bhabha first-order wave equations: I. C, P, and T, Phys. Rev. D 10(12) (1974) 4049-4063.
  • [6] Y. Nedjadi, and R.C. Barrett, On the properties of the Duffin-Kemmer-Petiau equation, J. Phys. G: Nucl. Part. Phys. 19 (1993) 87-98.
  • [7] V.Ya. Fainberg, and B.M. Pimentel, On equivalence of Duffin-Kemmer-Petiau and Klein- Gordon equations, B. J. Phys. 30(2) (2000) 275-281.
  • [8] J.T. Lunardi, B.M. Pimentel, R.G. Teixeira, and J.S. Valverde, Remarks on Duffin-Kemmer- Petiau theory and gauge invariance, Phys. Lett. A 268(3) (2000) 165-173.
  • [9] L. Chetouani, M. Merad, T. Boudjedaa, and A. Lecheheb, Solution of Duffin-Kemmer-Petiau equation for the step potential, Int. J. Theor. Phys. 43(4) (2004) 1147-1159.
  • [10] M. Merad, DKP equation with smooth potential and position-dependent mass, Int. J. Theor. Phys. 46(8) (2007) 2105-2118.
  • [11] B. Boutabia-Ch ́eraitia, and T. Boudjedaa, The Green function for the Duffin-Kemmer- Petiau equation, J. Geom. Phys. 62(10) (2012) 2038-2043.
  • [12] J.T. Lunardi, A note on the Duffin-Kemmer-Petiau equation in (1 + 1) space-time dimen- sions, J. Math. Phys. 58 (2017) 123501.
  • [13] V.B. Berestetskii, E.M. Lifshitz, and L.P. Pitaevskii, Quantum electrodynamics, Pergamon Press Ltd., Headingt.on Hill Hall, Oxford OX3 OBW, England. Vol 4. 2nd ed (1982).
  • [14] D. Bouchefra, and B. Boudjedaa, The explicit relation between the DKP equation and the Klein-Gordon equation, to appear in AIP Conference Proceedings of Third International Conference of Mathematical Sciences (ICMS 2019).
There are 14 citations in total.

Details

Primary Language English
Subjects Software Engineering (Other)
Journal Section Articles
Authors

Djahida Bouchefra 0000-0003-1616-765X

Badredine Boudjedaa This is me

Publication Date December 29, 2019
Acceptance Date December 20, 2019
Published in Issue Year 2019 Volume: 1 Issue: 2

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