Revista Integración, temas de matemáticas.
Vol. 42 No. 1 (2024): Revista Integración, temas de matemáticas
Accepted articles: Preprint

q−Relativistic wave equation of the form i∂^q·ψq + mψ_0 = Eψ

Julio Cesar Jaramillo-Quiceno
Universidad Nacional de Colombia

Published 2024-05-06

Keywords

  • q - Relativistic wave equation,
  • Separation of variables,
  • Fermionic and bosonic solutions,
  • Lorentz coordinates

How to Cite

Jaramillo Quiceno, J. C. (2024). q−Relativistic wave equation of the form i∂^q·ψq + mψ_0 = Eψ. Revista Integración, Temas De matemáticas, 42(1), 31–42. https://doi.org/10.18273/revint.v42n1-2024003

Abstract

In this paper we introduce a q relativistic wave equation of the form i∂^q·ψq + mψ_0 = Eψ. We present the q-spinorial solutions using the method of separated variables in the q-relativistic wave equation. Some comments are mentioned at the end of the paper.

Downloads

Download data is not yet available.

References

  1. W. Gordon, Phys 40, pp. 117â-133, (1926 -1927).
  2. O. Klein, "Quantum Theory and Five-Dimensional Theory of Relativity", Phys 37, (1926) pp. 895â-906, dx.doi.org/10.1007/BF01397481.
  3. G. Petiau, Acad. R. Belg. Cl. Sci. Mem, Collect. (8) 16, No. 2. (1936).
  4. R. Duffin, "On The Characteristic Matrices of Covariant Systems", Phys. Rev. C (1938), 54, 1114. dx.doi.org/10.1103/PhysRev.54.1114.
  5. N, "The Particle Aspect of Meson Theory", Proc. R. Soc. Lond. A., 173, (1939), pp. 91â-116. doi: 10.1098/rspa.1939.0131.
  6. A. Okninski, "Duffin â Kemmer âPetiau and Dirac Equations", A Supersymmetric Connection, Sym, 4, (2012). pp. 427–440; doi:10.3390/sym4030427.
  7. A. J. Proca, Phys. Radium (7) 8, (1936), pp. 347–353.
  8. P. A. M. Dirac, "Quantum Theory of Electron" ,Proc. R. Soc. Lond. A. 117, (1928), doi: 10.1098/rspa.1928.0023.
  9. M. Fierz and W. Pauli, "On relativistic wave equations for particles of arbitrary spin in an electromagnetic field", Proc. R. Soc. Lond. A 173, (1939), doi: 10.1098/rspa.1939.0140.
  10. W. Rarita and J. Schwinger, " On a Theory of Particles with Half-Integral Spin", Phys. Rev. (60) 61 (1941). dx.doi.org/10.1103/PhysRev.60.61.
  11. H. J. Bhabha, "Relativistic Wave Equations for the Elementary Particles", Proc. Ind. Acad. Sci. A ,India.21. (1945), pp. 241 – 264. dx.doi.org/10.1103/RevModPhys.17.200.
  12. J. Niederle and A. Nikitin, "Relativistic wave equations for interacting massive particles with arbitrary half-intreger spins", (2001) arXiv:hep-th/0412213v, doi: 10.1103/PhysRevD.64.125013.
  13. A. Silenko, "Verification of Relativistic Wave Equations for Spin-1 Particles", arXiv:hep-th/0401183v1.
  14. D. Kulikov, and R. Titik, " Relativistic wave equation for one spin-1/2 and one spin-0 particle", arXiv:0706.1010v1 [hep-th].
  15. M. Pillin, "q-Deformed Relativistic Wave Equations", J.Math.Phys. (1994) 35, pp. 2804–2817.
  16. J. C. Jaramillo, An Introduction to Spinor Differential and Integral Calculus from q− Lorentzian Algebra, Revista Integración, Temas De matemáticas, 41(1)(2023), 45–60. https://doi.org/10.18273/revint.v41n1-2023003.
  17. Schmidke, W. B., Wess, J., and Zumino, B. "A q− deformed Lorentz algebra", preprint MPI-Ph/91-15, to be published in Z. Phys. C Particles and Fields.
  18. A. Schmidt and H. Wachter, "Spinor calculus for q-deformed quantum spaces I ", e-Print: 0705.1640 [hep-th], arXiv:0705.1640 [hep-th].
  19. Beretetskii, V. B., Lifshitz, E, M., and Pitaekskii, L, P., "Relativistic Quantum Theory, Volume 4 of course of theoretical physics, part one", Pergamon press, (1971).
  20. Mansour, T and Schork, M, "Commutation Relations, Normal Ordering, and Stirling Numbers". CRC press Taylor and Francis group, (2016), p .229 .