Skip to main content
SpringerLink
Log in

Imagery of symmetry in current physics

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

We consider a remarkable symmetry duality that is broken under a phase transition permitting the appearance of superconductivity and superfluidity. This is a wine-bottle rotation symmetry in a semiphenomenological description in the spirit of Ginzburg and Landau, while it is a phase symmetry responsible for the conservation of the number of particles (helium atoms, Cooper electron pairs) in Bogoliubov’s quantum theory. This duality is interesting in the context of the contraposition of logic and intuition or Science and Art. We also briefly discuss another aspect of distorted symmetry connected with varying the geometry of space-time and with dimensional reduction in particular.

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. L. D. Landau, Phys. Z. Sowjetunion, 11, 26–47 (1937).

    MATH  Google Scholar 

  2. N. N. Bogoliubov, J. Phys. (USSR), 11, 23–32 (1947); Sov. Phys. Usp., 93, 552–564 (1967).

  3. D. V. Shirkov, Found. Phys., 16, 27–38 (1986).

    Article  MathSciNet  ADS  Google Scholar 

  4. L. D. Landau, Sov. JETP, 11, 71–89 (1941); Sov. Phys. Usp., 97, 495 (1967).

    Google Scholar 

  5. P. C. Hohenberg and P. M. Platzman, Phys. Rev. Lett., 152, 198–200 (1966); L. Aleksandrov, V. A. Zagrebnov, Zh.A. Kozlov, V. A. Parfenov, and V. B. Priezzhev, 1975, 41, 915–918; M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, Science, 269, 198–201 (1995).

    ADS  Google Scholar 

  6. V. L. Ginzburg and L. D. Landau, Zh. Eksp. Teor. Fiz., 20, 1064–1081 (1950); English transl: “On the theory of superconductivity,” in: Collected Papers of L. D. Landau (D. Ter Haar, ed.), Pergamon, Oxford (1965), p. 546.

    Google Scholar 

  7. L. P. Gor’kov, Sov. Phys. JETP, 9, 1364–1367 (1959); 10, 998 (1960).

    MathSciNet  MATH  Google Scholar 

  8. N. N. Bogolyubov, Sov. Phys. JETP, 7, 41–46 (1958); Nuovo Cim., 7, 794–805 (1958).

    MATH  Google Scholar 

  9. N. N. Bogolyubov, Vestnik AN SSSR, 28, 25–29 (1958).

    Google Scholar 

  10. B. A. Arbuzov, A. N. Tavkhedidze, and R. N. Faustov, Sov. Phys. Dokl., 6, 598–599 (1962).

    ADS  Google Scholar 

  11. D. V. Shirkov, Phys. Usp., 52, 549–557 (2009); arXiv:0903.3194v2 [physics.hist-ph].

    Article  ADS  Google Scholar 

  12. I. Ya. Aref’eva, Phys. Lett. B, 328, 411–419 (1994); arXiv:hep-th/9306014v2 (1993).

    Article  ADS  Google Scholar 

  13. R. Kirschner, L. N. Lipatov, and L. Szymanowski, Nucl. Phys. B, 425, 579–594 (1994); arXiv:hep-th/9402010v1 (1994).

    Article  ADS  Google Scholar 

  14. D. V. Shirkov, Phys. Part. Nucl. Lett., 7, 379–383 (2010); arXiv:1004.1510v3 [hep-th] (2010).

    Article  Google Scholar 

  15. P. P. Fiziev and D. V. Shirkov, Theor. Math. Phys., 167, 680–691 (2011); arXiv:1009.5309v2 [hep-th] (2010).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia

    D. V. Shirkov

Authors
  1. D. V. Shirkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. V. Shirkov.

Additional information

Dedicated to the memory of Albert Nikiforovich Tavkhelidze

Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 170, No. 2, pp. 292–303, February, 2012.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shirkov, D.V. Imagery of symmetry in current physics. Theor Math Phys 170, 239–248 (2012). https://doi.org/10.1007/s11232-012-0026-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11232-012-0026-5

Keywords

Search

Navigation