Skip to main content
SpringerLink
Log in

Quantum phase effects for electrically charged particles: converging descriptions via fields and potentials

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

We analyze the physical meaning of quantum phase effects from a new perspective, related to our recent disclosure of two novel quantum phases for electric/magnetic dipoles – in addition to the previously known Aharonov-Casher and He-McKellar-Wilkens phases, and two novel quantum phases for point-like charged particles – in addition to the electric and magnetic Aharonov-Bohm phases. We show that the obtained complete expression for the quantum phase of a moving charge in an EM field allows to establish its direct link with the interactional electromagnetic momentum in the system “particle and external field” and to better understand the physical meaning of quantum phase effects, which is discussed using a number of particular examples.

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

Fig. 1

Similar content being viewed by others

Data availability statement

All data generated or analyzed during this study are included in this published article.

Notes

  1. We notice that Eq. (28) also holds for the bound electron in hydrogenlike atoms with the appropriate expression for the interactional EM field momentum [28, 29].

References

  1. Y. Aharonov, D. Bohm, Phys. Rev. 115, 485 (1959)

    Article  ADS  MathSciNet  Google Scholar 

  2. Y. Aharonov, D. Bohm, Phys. Rev. 123, 1511 (1961)

    Article  ADS  MathSciNet  Google Scholar 

  3. A. Tonomura, N. Osakabe, T. Matsuda et al., Phys. Rev. A 34, 815 (1986)

    Article  ADS  Google Scholar 

  4. M. Peshkin, A. Tonomura, The Aharonov-Bohm Effect (Springer-Verlag, Berlin, 1989)

    Book  Google Scholar 

  5. Y. Aharonov, D. Rohrlich, Quantum Paradoxes: Quantum Theory for the Perplexed (Wiley, Weinheim, 2005)

    Book  Google Scholar 

  6. L. Vaidman, Phys. Rev. A 86, 040101 (2012)

    Article  ADS  Google Scholar 

  7. Y. Aharonov, E. Cohen, D. Rohrlich, Phys. Rev. A 92, 026101 (2015)

    Article  ADS  Google Scholar 

  8. L. Vaidman, Phys. Rev. A 92, 026102 (2015)

    Article  ADS  Google Scholar 

  9. P. Pearle, C.A. Rizzi, Phys. Rev. A 95, 052124 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  10. A.L. Kholmetskii, O.V. Missevitch, T. Yarman, Sci. Rep. 8, 11937 (2018)

    Article  ADS  Google Scholar 

  11. L.D. Landau, E.M. Lifshitz, Quantum Mechanics. Non-relativistic Theory (Elsevier 1981).

  12. H. Batelaan, A. Tonomura, Phys. Today 62, 38 (2009)

    Article  Google Scholar 

  13. Y. Aharonov, A. Casher, Phys. Rev. Lett. 53, 319 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  14. X.-G. He, B.H.J. McKellar, Phys. Rev. A 47, 3424 (1993)

    Article  ADS  Google Scholar 

  15. M. Wilkens, Phys. Rev. Lett. 72, 5 (1994)

    Article  ADS  Google Scholar 

  16. M. Koenig et al., Phys. Rev. Lett. 96, 076804 (2006)

    Article  ADS  Google Scholar 

  17. J. Gillot et al., Phys. Rev. Lett. 111, 030401 (2013)

    Article  ADS  Google Scholar 

  18. W. Shockley, R.P. James, Phys. Rev. Lett. 18, 876 (1967)

    Article  ADS  Google Scholar 

  19. S. Goleman, J.H. Van Vleck, Phys. Rev. 171, 1370 (1968)

    Article  ADS  Google Scholar 

  20. Y. Aharonov, P. Pearle, L. Vaidman, Phys. Rev. A 37, 4052 (1988)

    Article  ADS  Google Scholar 

  21. A.L. Kholmetskii, O.V. Missevitch, T. Yarman, EPL 113, 14003 (2016)

    Article  ADS  Google Scholar 

  22. A.L. Kholmetskii, O.V. Missevitch, T. Yarman, Ann. Phys. 36, 139 (2016)

    Article  ADS  Google Scholar 

  23. M. Fabrizio, A. Morri, Electromagnetism of Continuous Media (Oxford University Press, Oxford, 2003)

    Book  Google Scholar 

  24. A.L. Kholmetskii, T. Yarman, EPL 120, 40007 (2017)

    Article  ADS  Google Scholar 

  25. A.L. Kholmetskii, O.V. Missevitch, T. Yarman, Ann. Phys. 392, 49 (2018)

    Article  ADS  Google Scholar 

  26. A.L. Kholmetskii, O.V. Missevitch, T. Yarman, Ann. Phys. 434, 168627 (2021)

    Article  Google Scholar 

  27. L.D. Landau, E.M. Lifshitz, The Classical Theory of Fields, 2nd edn. (Pergamon Press, New York, 1962)

    MATH  Google Scholar 

  28. T. Yarman, Found. Phys. Lett. 19, 675 (2006)

    Article  MathSciNet  Google Scholar 

  29. A.L. Kholmetskii, T. Yarman, Z. Naturforsch. 73(7), 565–577 (2018)

    Article  ADS  Google Scholar 

  30. A. Miffre, M. Jacquey, M. Büchner et al., Eur. Phys. J. D 38, 353 (2006)

    Article  ADS  Google Scholar 

  31. S. Lepoutre, A. Gauguet, G. Trnec et al., Phys. Rev. Lett. 109, 120404 (2012)

    Article  ADS  Google Scholar 

  32. Ch. Overstreet, P. Asenbaum, J. Curti et al., Science 375, 226 (2022)

    Article  ADS  MathSciNet  Google Scholar 

  33. E. Li, B.J. Eggleton, K. Fang, S. Fan, Nature commun. 5(1), 1–5 (2014)

    ADS  Google Scholar 

  34. C. Marletto, V. Vedral, Phys. Rev. Lett. 125, 040401 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  35. C. Teitelboim, D. Villarroel, C.G. Van Weert, Riv. Nuovo Cim 3(9), 1–60 (1980)

    Article  ADS  Google Scholar 

  36. J.D. Jackson, Classical Electrodynamics, 3rd edn. (Wiley, New York, 1998)

    MATH  Google Scholar 

Download references

Acknowledgements

We thank the anonymous referee for useful comments and suggestions, which have been taken into account for the improvement of the final version of the paper.

Author information

Authors and Affiliations

  1. Department of Physics, Belarusian State University, Minsk, Belarus

    A. L. Kholmetskii

  2. Institute for Nuclear Problems, Belarusian State University, Minsk, Belarus

    O. Missevitch

  3. Istanbul Okan University, Istanbul, Turkey

    T. Yarman

  4. Savronik, Eskisehir, Turkey

    T. Yarman

Authors
  1. A. L. Kholmetskii
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. O. Missevitch
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. T. Yarman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. L. Kholmetskii.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kholmetskii, A.L., Missevitch, O. & Yarman, T. Quantum phase effects for electrically charged particles: converging descriptions via fields and potentials. Eur. Phys. J. Plus 137, 387 (2022). https://doi.org/10.1140/epjp/s13360-022-02590-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-022-02590-1

Search

Navigation