Skip to main content
SpringerLink
Log in

Zitterbewegung in External Magnetic Field: Classic versus Quantum Approach

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

We investigate variations of the Zitterbewegung frequency of electron due to an external static and uniform magnetic field employing the expectation value quantum approach, and compare our results with the classical model of spinning particles. We demonstrate that these two so far compatible approaches are not in agreement in the presence of an external uniform static magnetic field, in which the classical approach breaks the usual symmetry of free particles and antiparticles states, i.e. it leads to CP violation. Hence, regarding the Zitterbewegung frequency of electron, the classical approach in the presence of an external magnetic field is unlikely to correctly describe the spin of electron, while the quantum approach does, as expected. We also show that the results obtained via the expectation value are in close agreement with the quantum approach of the Heisenberg picture derived in the literature. However, the method we use is capable of being compared with the classical approach regarding the spin aspects. The classical interpretation of spin produced by the altered Zitterbewegung frequency, in the presence of an external magnetic field, are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Dirac, P.A.M.: Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci. 117, 610–624 (1928)

    Article  ADS  MATH  Google Scholar 

  2. Dirac, P.A.M.: Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci. 118, 351–361 (1928)

    Article  ADS  MATH  Google Scholar 

  3. Dirac, P.A.M.: The Principles of Quantum Mechanics, 4th edn. Oxford University Press, Oxford (1958)

    MATH  Google Scholar 

  4. Rose, M.E.: Relativistic Electron Theory. Wiley, New York (1961)

    MATH  Google Scholar 

  5. Bjorken, J.D., Drell, S.D.: Relativistic Quantum Mechanics. McGraw-Hill, New York (1964)

    Google Scholar 

  6. Sakurai, J.J.: Advanced Quantum Mechanics. Pearson Education, Delhi (1967)

    Google Scholar 

  7. Itzykson, C., Zuber, J.-B.: Quantum Field Theory. McGraw-Hill, Singapore (1980)

    Google Scholar 

  8. Greiner, W.: Relativistic Quantum Mechanics. Springer, Berlin (1990)

    MATH  Google Scholar 

  9. Merzbacher, E.: Quantum Mechanics, 3rd edn. Wiley, New York (1998)

    Google Scholar 

  10. Huang, K.: Am. J. Phys. 20, 479–484 (1952)

    Article  ADS  MATH  Google Scholar 

  11. Schrödinger, E.: Sitz. Preuss. Akad. Wiss. Phys. Math. Kl 24, 418–428 (1930)

    Google Scholar 

  12. Schrödinger, E.: Sitz. Preuss. Akad. Wiss. Phys. Math. Kl. 3, 1 (1931)

    Google Scholar 

  13. Barut, A.O., Bracken, A.J.: Phys. Rev. D 23, 2454–2463 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  14. Newton, T.D., Wigner, P.: Rev. Mod. Phys. 21, 400–406 (1949)

    Article  ADS  MATH  Google Scholar 

  15. Rusin, T.M., Zawadzki, W.: J. Phys., Condens. Matter 19, 136219 (2007) [18 pages]

    Article  ADS  Google Scholar 

  16. Rusin, T.M., Zawadzki, W.: Phys. Rev. B 76, 195439 (2007) [7 pages]

    Article  ADS  Google Scholar 

  17. Bender, D., et al.: Phys. Rev. D 30, 515–527 (1984)

    Article  ADS  Google Scholar 

  18. Hestenes, D.: Found. Phys. 23, 365–387 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  19. Gordon, W.: Z. Phys. 50, 630–632 (1927)

    ADS  Google Scholar 

  20. Frenkel, J.: Wave Mechanics, Advanced General Theory. Oxford University Press, London (1934)

    MATH  Google Scholar 

  21. Barut, A.O., Bracken, A.J.: Phys. Rev. D 24, 3333–3334 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  22. Hestenes, D.: Found. Phys. 20, 1213–1232 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  23. Hestenes, D.: Found. Phys. 40, 1–54 (2010)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  24. Mathissen, M.: Acta Phys. Pol. A 6, 163–200 (1937)

    Google Scholar 

  25. Mathissen, M.: Acta Phys. Pol. A 6, 218 (1937)

    Google Scholar 

  26. Hönl, H.: Ann. Phys. 33, 565–585 (1938)

    Article  MATH  Google Scholar 

  27. Weyssenhof, J.W.: Nature 141, 328–329 (1938)

    Article  ADS  Google Scholar 

  28. Weyssenhof, J.W.: Acta Phys. Pol. A 9, 47–53 (1947)

    Google Scholar 

  29. Brandmüller, J.: Naturwissenschaften 38, 139–139 (1951)

    Article  ADS  Google Scholar 

  30. Plyushchay, M.S.: Phys. Lett. B 236, 291–297 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  31. Salesi, G., Recami, E.: Phys. Lett. A 267, 219–224 (2000)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  32. Pryce, M.H.L.: Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci. 195, 62–81 (1948)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  33. Foldy, L.L., Wouthuysen, S.A.: Phys. Rev. 78, 29–36 (1950)

    Article  ADS  MATH  Google Scholar 

  34. Tani, S.: Prog. Theor. Phys. 6, 267–285 (1951)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  35. Feshbach, H., Villars, F.: Rev. Mod. Phys. 30, 24–25 (1958)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  36. Barut, A.O., Malin, S.: Rev. Mod. Phys. 40, 632–651 (1968)

    Article  ADS  MATH  Google Scholar 

  37. Lock, J.A.: Am. J. Phys. 47, 797–802 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  38. Krekora, P., Su, Q., Grobe, R.: Phys. Rev. Lett. 93, 043004 (2004) [4 pages]

    Article  ADS  Google Scholar 

  39. Barut, A.O., Zanghi, N.: Phys. Rev. Lett. 52, 2009–2012 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  40. Klishevich, S., Plyushchay, M.: Phys. Lett. B 459, 201–207 (1999)

    Article  ADS  Google Scholar 

  41. Recami, E., Salesi, G.: Phys. Rev. A 57, 98–105 (1998)

    Article  ADS  Google Scholar 

  42. Salesi, G.: Int. J. Mod. Phys. A 17, 347–374 (2002)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  43. Barut, A.O., Pavšič, M.: Class. Quantum Gravity 4, L131–L136 (1987)

    Article  ADS  Google Scholar 

  44. Recami, E., Salesi, G.: Field theory of the electron: spin and Zitterbewegung. In: Pronin, P.I., Sardanashvily, G.A. (eds.) Particles, Gravity and Space–Time, pp. 345–368. World Scientific, Singapore (1996). hep-th/9508168

    Chapter  Google Scholar 

  45. Pavšič, M., Recami, E., Rodrigues, W.A. Jr.: Hadron. J. 18, 97–118 (1995)

    Google Scholar 

  46. Zawadzki, W.: In: Haidemenakis, E.D. (ed.) Optical Properties of Solides, p. 179. Gordon & Breach, New York (1970)

    Google Scholar 

  47. Cannata, F., Ferrari, L., Russo, G.: Solid State Commun. 74, 309–312 (1990)

    Article  ADS  Google Scholar 

  48. Ferrari, L., Russo, G.: Phys. Rev. B 42, 7454–7461 (1990)

    Article  ADS  Google Scholar 

  49. Zawadzki, W.: In: Landwehr, G., Ossau, W. (eds.) High Magnetic Fields in the Physics of Semiconductors II, p. 755. World Scientific, Singapore (1997)

    Google Scholar 

  50. Salesi, G.: Int. J. Mod. Phys. A 20, 2027–2036 (2005)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  51. Jiang, Z.F., Li, R.D., Zhang, S.C., Liu, W.M.: Phys. Rev. B 72, 045201 (2005) [5 pages]

    Article  ADS  Google Scholar 

  52. Zawadzki, W.: Phys. Rev. B 72, 085217 (2005) [4 pages]

    Article  ADS  Google Scholar 

  53. Zawadzki, W.: One-dimensional semirelativity for electrons in carbon nanotubes. cond-mat/0510184 [4 pages]

  54. Schliemann, J., Loss, D., Westervelt, R.M.: Phys. Rev. Lett. 94, 206801 (2005) [4 pages]

    Article  ADS  Google Scholar 

  55. Schliemann, J., Loss, D., Westervelt, R.M.: Phys. Rev. B 73, 085323 (2006) [9 pages]

    Article  ADS  Google Scholar 

  56. Katsnelson, M.I.: Eur. Phys. J. B 51, 157–160 (2006)

    Article  ADS  Google Scholar 

  57. Cserti, J., Dávid, G.: Phys. Rev. B 74, 172305 (2006) [4 pages]

    Article  ADS  MATH  Google Scholar 

  58. Vaishnav, J.Y., Clark, C.W.: Phys. Rev. Lett. 100, 153002 (2008) [4 pages]

    Article  ADS  Google Scholar 

  59. Brusheim, P., Xu, H.Q.: Catching the Zitterbewegung. arXiv:0810.2186 [cond-mat] [4 pages]

  60. Lamata, L., León, J., Schätz, T., Solano, E.: Phys. Rev. Lett. 98, 253005 (2007) [4 pages]

    Article  ADS  Google Scholar 

  61. Villavicencio, M., Roa-Neri, J.A.E.: Eur. J. Phys. 21, 119–123 (2000)

    Article  MATH  Google Scholar 

  62. van Holten, J.W.: Physica A 182, 279–292 (1992)

    Article  ADS  Google Scholar 

  63. van Holten, J.W.: Relativistic dynamics of spin in strong external fields. hep-th/9303124 [11 pages]

  64. Thirring, H.: Principles of Quantum Electrodynamics. Academic Press, New York (1958)

    Google Scholar 

  65. Van Dyck, R.S. Jr., Schwinberg, P.B., Dehmelt, H.G.: Phys. Rev. D 34, 722–736 (1986)

    Article  ADS  Google Scholar 

  66. Heavner, T.P., Jefferts, S.R., Donley, E.A., Shirley, J.H., Parker, T.E.: Metrologia 42, 411–422 (2005)

    Article  ADS  Google Scholar 

  67. Salesi, G., Recami, E.: Found. Phys. Lett. 10, 533–546 (1997)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Shahid Beheshti University, G. C., Evin, Tehran, 19839, Iran

    Mehran Zahiri-Abyaneh & Mehrdad Farhoudi

Authors
  1. Mehran Zahiri-Abyaneh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mehrdad Farhoudi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mehrdad Farhoudi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zahiri-Abyaneh, M., Farhoudi, M. Zitterbewegung in External Magnetic Field: Classic versus Quantum Approach. Found Phys 41, 1355–1374 (2011). https://doi.org/10.1007/s10701-011-9553-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10701-011-9553-4

Keywords

Search

Navigation