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

Yıl 2019, Cilt: 1 Sayı: 2, 69 - 76, 29.12.2019

Öz

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.





Destekleyen Kurum

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

Kaynakça

  • [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).
Yıl 2019, Cilt: 1 Sayı: 2, 69 - 76, 29.12.2019

Öz

Kaynakça

  • [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).
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Yazılım Mühendisliği (Diğer)
Bölüm Articles
Yazarlar

Djahida Bouchefra 0000-0003-1616-765X

Badredine Boudjedaa Bu kişi benim

Yayımlanma Tarihi 29 Aralık 2019
Kabul Tarihi 20 Aralık 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 1 Sayı: 2

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