Advertisement

The Relationship Between Complex Quantum Hamiltonian Dynamics and Krein Space Quantization

  • Farrin PayandehEmail author
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 184)

Abstract

Negative energy states are appeared in the structure of complex Hamiltonian dynamics. These states also play the main role in Krein space quantization to achieve a naturally renormalized theory. Here, we will have an overlook on the role of negative energy states in complex mechanics and Krein space. In a previous work, we have shown that the method of complex mechanics provides us some extra wave functions within complex spacetime. We have supported our method of including negative energy states, by referring to the theory of Krein space quantization that by taking the full set of Dirac solutions is able to remove the infinities of quantum field theory (QFT), naturally. Our main proposal here is that particles and antiparticles should be treated as physical entities with positive energy instead of considering antiparticles with negative energy and the unphysical particle and antiparticle with negative energy should be introduced as the complement of the sets of solutions for Dirac equation. Therefore, we infer that the Krein space method which is supposed as a pure mathematical approach, has root on the strong foundations of Hamilton-Jacobi equations and therefore on classical dynamics and it can successfully explain the reason why the renormalization procedure in QFT works.

Notes

Acknowledgments

The author would like to thank the organizers of PHHQP15, specially, Prof. Fabio Bagarello.

References

  1. 1.
    M.S. El Naschie, Int. J. Nonlinear Sci. Simul. 6, 95 (2005)Google Scholar
  2. 2.
    M.S. El Naschie, Chaos Solitons Fract. 5, 1031 (1995)ADSCrossRefGoogle Scholar
  3. 3.
    M.S. El Naschie, Chaos Solitons Fract. 5, 1551 (1995)ADSCrossRefGoogle Scholar
  4. 4.
    M.S. El Naschie, Chaos Solitons Fract. 11, 1149 (2000)ADSCrossRefGoogle Scholar
  5. 5.
    L. Sigalotti, G. Di, A. Mejias, Int. J. Nonlinear Sci. Numer. Simul. 7, 467 (2006)CrossRefGoogle Scholar
  6. 6.
    J. Czajko, Chaos Solitons Fract. 11, 1983 (2000)ADSCrossRefGoogle Scholar
  7. 7.
    C.D. Yang, Chaos Solitons Fract. 33, 1073 (2007)ADSCrossRefGoogle Scholar
  8. 8.
    C.D. Yang, Chaos Solitons Fract. 32, 274 (2007)ADSCrossRefGoogle Scholar
  9. 9.
    C.D. Yang, Ann. Phys. 319, 444 (2005)ADSCrossRefGoogle Scholar
  10. 10.
    C.D. Yang, Chaos Solitons Fract. 32, 312 (2007)ADSCrossRefGoogle Scholar
  11. 11.
    C.D. Yang, Ann. Phys. 319, 399 (2005)ADSCrossRefGoogle Scholar
  12. 12.
    C.D. Yang, CH. Wei, Chaos Solitons Fract. 33, 118 (2007)Google Scholar
  13. 13.
    C.D. Yang, Int. J. Nonlinear Sci. Numer. Simul. 8, 397 (2007)CrossRefGoogle Scholar
  14. 14.
    C.D. Yang, Chaos Solitons Fract. 30, 41 (2006)ADSCrossRefGoogle Scholar
  15. 15.
    C.D. Yang, Chaos Solitons Fract. 38, 316 (2008)ADSCrossRefGoogle Scholar
  16. 16.
    C.D. Yang, Ann. Phys. 321, 2876 (2006)ADSCrossRefGoogle Scholar
  17. 17.
    C.M. Bender, Proc. Inst. Math. NAS Ukrine 50(2), 617628 (2004)Google Scholar
  18. 18.
    F. Payandeh, J. Phys: Conf. Ser. 626, 012053 (2015)ADSGoogle Scholar
  19. 19.
    F. Payandeh, Mod. Phys. Lett. A. 29, 18 (2014)MathSciNetCrossRefGoogle Scholar
  20. 20.
    I. Antoniadis, J. Iliopoulos, T.N. Tomaras, Nucl. Phys. B 462, 437 (1996)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    T. Garidi et al, J. Math. Phys., 49, 032501 (2008); T. Garidi et al, J. Math. Phys., 44, 3838 (2003); S. Behroozi et al, Phys. Rev. D, 74, 124014 (2006)Google Scholar
  22. 22.
    J.P. Gazeau, J. Renaud, M.V. Takook, Class. Quant. Grav. 17, 1415 (2000), gr-qc/9904023Google Scholar
  23. 23.
    B. Allen, Phys. Rev. D 32, 3136 (1985)ADSMathSciNetCrossRefGoogle Scholar
  24. 24.
    M. Mintchev, J. Phys. A: Math. Gen. 13, 1841 (1979)ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    M.V. Takook, Mod. Phys. Lett A 16, 1691 (2001)ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    M.V. Takook, Int. J. Mod. Phys. E 11, 509 (2002). gr-qc/0006019Google Scholar
  27. 27.
    H.L. Ford, Quantum Field Theory in Curved Spacetime. gr-qc/9707062Google Scholar
  28. 28.
    S. Rouhani, M.V. Takook, Int. J. Theor. Phys. 48, 2740 (2009)MathSciNetCrossRefGoogle Scholar
  29. 29.
    F. Payandeh, M. Mehrafarin, S. Rouhani, M.V. Takook, UJP 53, 1203 (2008)Google Scholar
  30. 30.
    F. Payandeh, M. Mehrafarin, M.V. Takook, AIP Conf. Proc. 957, 249 (2007)ADSMathSciNetCrossRefGoogle Scholar
  31. 31.
    F. Payandeh, Rev. Cub. Fis. 26, 232 (2009)Google Scholar
  32. 32.
    F. Payandeh, J. Phys: Conf. Ser. 174, 012056 (2009)ADSGoogle Scholar
  33. 33.
    F. Payandeh, M. Mehrafarin, M.V. Takook, Sci. China Ser. G: Phys., Mech. Astron. 52, 212 (2009)ADSCrossRefGoogle Scholar
  34. 34.
    F. Payandeh, AIP Conf. Proc. 1246, 170 (2010)ADSCrossRefGoogle Scholar
  35. 35.
    F. Payandeh, J. Phys. Conf. Ser. 306, 012054 (2011)ADSCrossRefGoogle Scholar
  36. 36.
    F. Payandeh, ISRN High Energy Phys. 2012, 714823 (2012)CrossRefGoogle Scholar
  37. 37.
    F. Payandeh, Z. Gh, Moghaddam, M. Fathi, Fortschr. Phys. 60, 1086 (2012)Google Scholar
  38. 38.
    M. Dehghani et al., Phys. Rev. D, 77, 064028 (2008); M.V. Takook et al., J. Math. Phys. 51, 032503 (2010)Google Scholar
  39. 39.
    B. Forghan, M.V. Takook, A. Zarei, Krein regularization of QED. Ann. Phys. 327, 2388 (2012)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    A. Refaei, M.V. Takook, Phys. Lett. B 704, 326 (2011)ADSCrossRefGoogle Scholar
  41. 41.
    A. Refaei, M.V. Takook, Mod. Phys. Lett. A 26, 31 (2011)ADSMathSciNetCrossRefGoogle Scholar
  42. 42.
    H. Pejhan, M.R. Tanhayi, M.V. Takook, Ann. Phys. 341, 195 (2014)ADSMathSciNetCrossRefGoogle Scholar
  43. 43.
    N.H. Barth, S.M. Christensen, Phys. Rev. D 28, 1876 (1983)ADSMathSciNetCrossRefGoogle Scholar
  44. 44.
    P. Horva, Phys. Rev. D 79, 084008 (2009). arXiv:0901.3775 ADSMathSciNetCrossRefGoogle Scholar
  45. 45.
    M. Kaku, Quantum Field Theory, A Modern Introduction (Oxford University Press, Oxford, 1993)Google Scholar
  46. 46.
    E. Peskin, D.V. Schroeder, An Introduction in Quantum Field Theory (Perseus Books, 1995)Google Scholar
  47. 47.
    F. Payandeh, J. Phys: Conf. Ser. 306, 012054 (2011)ADSGoogle Scholar
  48. 48.
    A. Zarei, M.V. Takook, B. Forghan, INT. J. Theor. Phys. 50, 2460 (2011)MathSciNetCrossRefGoogle Scholar
  49. 49.
    O. Klein, Z. Phys. 53, 157 (1929)ADSCrossRefGoogle Scholar
  50. 50.
    F. Payandeh, T. Mohammad Pur, M. Fathi, Z.Gh. Moghaddam, Chin. Phys. C 37, 113103 (2013)Google Scholar
  51. 51.
    N.I. Guang-jiong, H. Guan. arXiv:quant-ph/9901046v1
  52. 52.
    M.O. Scully, H. Walther, Phys. Rev. A 49, 3 (1994)MathSciNetCrossRefGoogle Scholar
  53. 53.
    T. Calarco, M. Cini, R. Onofrio, EPL 47, 407 (1999)ADSMathSciNetCrossRefGoogle Scholar
  54. 54.
    P.A.M. Dirac, Bakerian lecture Proc. Roy. Soc. Lond. A 180, 1 (1942)ADSMathSciNetCrossRefGoogle Scholar
  55. 55.
    P.A.M. Dirac, Nobel lecture, Dec 12 (1933)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of PhysicsPayame Noor University (PNU)TehranIran

Personalised recommendations