Skip to main content
SpringerLink
Log in

On geometric interpretation of the Aharonov–Bohm effect

  • Elementary Particle Physics and Field Theory
  • Published:
Russian Physics Journal Aims and scope

A geometric interpretation of the Aharonov–Bohm effect is given in terms of connections on principal fiber bundles. It is demonstrated that the principal fiber bundle can be trivial while the connection and its holonomy group are nontrivial. Therefore, the main role is played by geometric rather than topological effects.

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. Y. Aharonov and D. Bohm, Phys. Rev., 115 (3), 485–491 (1959).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. F. G. Werner and D. R. Brill, Phys. Rev. Lett., 4 (7), 344–347 (1960).

    Article  ADS  Google Scholar 

  3. R. G. Chambers, Phys. Rev. Lett., 5 (1), 3–5 (1960).

    Article  MathSciNet  ADS  Google Scholar 

  4. H. Boersch, H. Hamisch, D. Wohlleben, and K. Grohmann, Z. Phys., 159, 397–404 (1960).

    Article  ADS  Google Scholar 

  5. M. V. Berry, Proc. Roy. Soc. London, A392 (1802), 45–57 (1984).

    ADS  Google Scholar 

  6. M. Katanaev, Russ. Phus. J., No. 3, 342–353 (2011).

  7. E. Schrödinger, Ann. Phys. Leipzig, 79 (4), 361–376 (1926).

    Article  MATH  Google Scholar 

  8. E. Schrödinger, Ann. Phys. Leipzig, 79 (6), 489–527 (1926).

    Article  MATH  Google Scholar 

  9. S. Kobayashi and K. Nomizu, Foundations of Differential Geometry. Vols. 1 and 2, Interscience Publishers, New York; London (1963).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. V. A. Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia

    M. O. Katanaev

Authors
  1. M. O. Katanaev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. O. Katanaev.

Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 3–9, May, 2011.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Katanaev, M.O. On geometric interpretation of the Aharonov–Bohm effect. Russ Phys J 54, 507–514 (2011). https://doi.org/10.1007/s11182-011-9646-8

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11182-011-9646-8

Keywords

Search

Navigation