Skip to main content
Log in

Dirac and Weyl Fermions: from the Gor’kov equations to the standard model

  • Methods of Theoretical Physics
  • Published:
JETP Letters Aims and scope Submit manuscript

Abstract

Gor’kov theory of superconductivity [L. P. Gor’kov, Sov. Phys. JETP 7, 505 (1958)] opened the application of the methods of quantum field theory to condensed matter physics. Later the results became relevant to relativistic quantum fields.

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

Access this article

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. P. Gor’kov, in BCS: 50 Years, Ed. by L. N. Cooper and D. Feldman (World Scientific, Singapore, 2011).

  2. L. P. Gor’kov, Sov. Phys. JETP 7, 505 (1958).

  3. Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122, 345 (1961).

    Article  ADS  Google Scholar 

  4. V. G. Vaks and A. I. Larkin, Sov. Phys. JETP 13, 192 (1961).

    Google Scholar 

  5. P. W. Anderson, Phys. Rev. 130, 439 (1963).

    Article  MathSciNet  ADS  Google Scholar 

  6. P. W. Higgs, Phys. Rev. Lett. 13, 508 (1964).

    Article  MathSciNet  ADS  Google Scholar 

  7. G. E. Volovik and L. P. Gor’kov, JETP Lett. 39, 674 (1984).

    ADS  Google Scholar 

  8. G. E. Volovik and L. P. Gor’kov, Sov. Phys. JETP 61, 843 (1985).

    Article  Google Scholar 

  9. C. D. Froggatt and H. B. Nielsen, Origin of Symmetry (World Scientific, Singapore, 1991).

    Book  Google Scholar 

  10. P. Horava, Phys. Rev. Lett. 95, 016405 (2005).

    Article  ADS  Google Scholar 

  11. G. E. Volovik, The Universe in a Helium Droplet (Clarendon, Oxford, 2003).

    MATH  Google Scholar 

  12. Y. Nambu, Phys. Rev. 117, 648 (1960).

    Article  MathSciNet  ADS  Google Scholar 

  13. L. P. Gor’kov, Sov. Sci. Rev. A Phys. 9, 1 (1987).

    Google Scholar 

  14. P. G. Grinevich and G. E. Volovik, J. Low Temp. Phys. 72, 371 (1988).

    Article  ADS  Google Scholar 

  15. T. Mizushima, Ya. Tsutsumi, T. Kawakami, M. Sato, M. Ichioka, and K. Machida, J. Phys. Soc. Jpn. 85, 022001 (2016).

    Article  ADS  Google Scholar 

  16. M. Sato and Y. Ando, arXiv:1608.03395.

  17. L. P. Gor’kov, JETP Lett. 40, 1155 (1984).

    ADS  Google Scholar 

  18. D. F. Agterberg, V. Barzykin, and L. P. Gor’kov, Phys. Rev. B 60, 14868 (1999).

    Article  ADS  Google Scholar 

  19. G. E. Volovik and V. P. Mineev, Sov. Phys. JETP 56, 579 (1982).

    Google Scholar 

  20. G. E. Volovik, JETP Lett. 46, 98 (1987).

    ADS  Google Scholar 

  21. H. B. Nielsen and M. Ninomiya, Nucl. Phys. B 185, 20 (1981).

    Article  ADS  Google Scholar 

  22. H. B. Nielsen and M. Ninomiya, Nucl. Phys. B 193, 173 (1981).

    Article  ADS  Google Scholar 

  23. M. Creutz, J. High Energy Phys. 0804, 017 (2008).

    Article  ADS  Google Scholar 

  24. M. Creutz, Ann. Phys. 342, 21 (2014).

    Article  ADS  Google Scholar 

  25. F. R. Klinkhamer and G. E. Volovik, JETP Lett. 80, 343 (2004).

    Article  ADS  Google Scholar 

  26. F. R. Klinkhamer and G. E. Volovik, Int. J. Mod. Phys. A 20, 2795 (2005).

    Article  ADS  Google Scholar 

  27. B. Lampe, Mod. Phys. Lett. A 28, 1350018 (2013).

    Article  ADS  Google Scholar 

  28. B. Lampe, arXiv:1505.03477.

  29. L. P. Gor’kov and G. B. Teitel’baum, J. Phys.: Conf. Ser. 108, 012009 (2008).

    Google Scholar 

  30. V. V. Dmitriev, A. A. Senin, A. A. Soldatov, and A. N. Yudin, Phys. Rev. Lett. 115, 165304 (2015).

    Article  ADS  Google Scholar 

  31. G. E. Volovik, J. Phys. C 21, L221 (1988).

    Article  ADS  Google Scholar 

  32. P. Muzikar and D. Rainer, Phys. Rev. B 27, 4243 (1983).

    Article  ADS  Google Scholar 

  33. K. A. Moler, D. J. Baar, J. S. Urbach, R. Liang, W. N. Hardy, and A. Kapitulnik, Phys. Rev. Lett. 73, 2744 (1994).

    Article  ADS  Google Scholar 

  34. S. Adler, Phys. Rev. 177, 2426 (1969).

    Article  ADS  Google Scholar 

  35. J. S. Bell and R. Jackiw, Nuovo Cim. A 60, 47 (1969).

    Article  ADS  Google Scholar 

  36. T. D. C. Bevan, A. J. Manninen, J. B. Cook, J. R. Hook, H. E. Hall, T. Vachaspati, and G. E. Volovik, Nature 386, 689 (1997).

    Article  ADS  Google Scholar 

  37. N. B. Kopnin, G. E. Volovik, and Ü. Parts, Europhys. Lett. 32, 651 (1995).

    Article  ADS  Google Scholar 

  38. N. B. Kopnin and M. M. Salomaa, Phys. Rev. B 44, 9667 (1991).

    Article  ADS  Google Scholar 

  39. G. E. Volovik, JETP Lett. 93, 66 (2011); arXiv:1011.4665.

    Article  ADS  Google Scholar 

  40. A. A. Burkov and L. Balents, Phys. Rev. Lett. 107, 127205 (2011).

    Article  ADS  Google Scholar 

  41. A. A. Burkov, M. D. Hook, and L. Balents, Phys. Rev. B 84, 235126 (2011).

    Article  ADS  Google Scholar 

  42. G. E. Volovik, JETP Lett. 104, 201 (2016); arXiv:1509.05006.

    Article  ADS  Google Scholar 

  43. S. Ryu and Y. Hatsugai, Phys. Rev. Lett. 89, 077002 (2002).

    Article  ADS  Google Scholar 

  44. A. P. Schnyder and S. Ryu, Phys. Rev. B 84, 060504(R) (2011).

    Article  ADS  Google Scholar 

  45. H. So, Prog. Theor. Phys. 74, 585 (1985).

    Article  ADS  Google Scholar 

  46. K. Ishikawa and T. Matsuyama, Z. Phys. C 33, 41 (1986).

    Article  ADS  Google Scholar 

  47. K. Ishikawa and T. Matsuyama, Nucl. Phys. B 280, 523 (1987).

    Article  ADS  Google Scholar 

  48. G. E. Volovik, Sov. Phys. JETP 67, 1804 (1988).

    Google Scholar 

  49. G. E. Volovik, JETP Lett. 70, 609 (1999); condmat/ 9909426.

    Article  ADS  Google Scholar 

  50. N. Read and D. Green, Phys. Rev. B 61, 10267 (2000).

    Article  ADS  Google Scholar 

  51. D. A. Ivanov, Phys. Rev. Lett. 86, 268 (2001).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to G. E. Volovik.

Additional information

In memory of Lev Petrovich Gor’kov

The article is published in the original.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Volovik, G.E. Dirac and Weyl Fermions: from the Gor’kov equations to the standard model. Jetp Lett. 105, 273–277 (2017). https://doi.org/10.1134/S0021364017040063

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0021364017040063

Navigation