Skip to main content
SpringerLink
Log in

Chern numbers, quaternions, and Berry's phases in Fermi systems

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

Yes, but some parts are reasonably concrete.

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. Berry, M.V.: Proc. Roy. Soc. London A392, 45 (1984)

    Google Scholar 

  2. Simon, B.: Phys. Rev. Lett.51, 2167 (1983)

    Google Scholar 

  3. Wilczek, F., Zee, A.: Phys. Rev. Lett.52, 2111 (1984)

    Google Scholar 

  4. Mead, C. A.: Phys. Rev. Lett.59, 161 (1987)

    Google Scholar 

  5. Avron, J., Sadun, L., Segert, J., Simon, B.: Phys. Rev. Lett.61, 1329 (1988)

    Google Scholar 

  6. Avron, J. E., Seiler, R., Yaffe, L. G.: Commun. Math. Phys.110, 110 (1987)

    Google Scholar 

  7. Kato, T.: J. Phys. Soc. J. Jpn.5, 435 (1950)

    Google Scholar 

  8. Choquet-Bruhat, Y., DeWitt-Morette, C., Dillard-Bleick, M.: Analysis, Manifolds and Physics, rev ed. Amsterdam: North Holland 1982

    Google Scholar 

  9. Kobayashi, S., Nomizu, K.: Foundations of differential geometry, vol. I and II. New York: John Wiley 1963, 1969

    Google Scholar 

  10. Atiyah, M.F.: Geometry of Yang-Mills fields, Lezioni Fermiane. Pisa: Accademia Nazionale dei Lincei & Scuola Normale Superiore 1979

    Google Scholar 

  11. Chern, S. S.: Complex manifolds without potential theory, sec. ed. Berlin, Heidelberg, New York: Springer 1979

    Google Scholar 

  12. Zee, A.: Phys. Rev. A38, 1 (1988)

    Google Scholar 

  13. Tinkham, M.: Group theory and quantum mechanics. New York: McGraw-Hill 1964

    Google Scholar 

  14. Bjorken, J. D., Drell, S. D.: Relativistic quantum mechanics. New York: McGraw-Hill 1964;

    Google Scholar 

  15. Itzykson, C., Zuber, J. B.: Quantum field theory. New York: McGraw-Hill 1980

    Google Scholar 

  16. Wigner, E. P.: Göttinger Nachr.31, 546 (1932); Wigner, E. P.: Group Theory. New York: Academic Press 1959

    Google Scholar 

  17. Frobenius, Schur: Berl. Ber., p. 186 (1906)

  18. Dyson, F.: J. Math. Phys.3, 140 (1964)

    Google Scholar 

  19. Mehta, M. L.: Random matrices and the statistical theory of energy levels. New York: Academic Press 1967

    Google Scholar 

  20. Kramers, H.A.: Proc. Acad. Amsterdam33, 959 (1930)

    Google Scholar 

  21. Adams, J.F.: Lectures on Lie Groups. Chicago: University of Chicago Press 1969

    Google Scholar 

  22. Bröcker, T., tom Dieck, T.: Representations of compact Lie groups. Berlin, Heidelberg, New York: Springer 1985

    Google Scholar 

  23. Sadun, L., Segert, J.: J. Phys. A22, L 111 (1989)

    Google Scholar 

  24. von Neumann, J., Wigner, E.P.: Phys. Zeit.30, 467 (1929)

    Google Scholar 

  25. Friedland, S., Robbin, J. W., Sylvester, J. H.: On the crossing rule. Commun. Pure Appl. Math.37, 19 (1984)

    Google Scholar 

  26. Mermin, N. D.: Rev. Mod. Phys.51, No. 3 (1979)

  27. Avron, J., Seiler, R., Simon, B.: Phys. Rev. Lett.51, 51 (1983)

    Google Scholar 

  28. Steenrod, N.: The topology of fibre bundles. Princeton: Princeton University Press 1951

    Google Scholar 

  29. Bott, R., Tu, L. W.: Differential forms in algebraic topology. Berlin, Heidelberg, New York: Springer 1982

    Google Scholar 

  30. Herzberg, G., Longuet-Higgins, H. C.: Discuss. Faraday Soc.55, 77 (1963)

    Google Scholar 

  31. Milnor, J. W., Stasheff, J. D.: Characteristic classes. Princeton, NJ: Princeton University Press 1974

    Google Scholar 

  32. Thouless D., et. al.: Phys. Rev. Lett.49, 405 (1982)

    Google Scholar 

  33. Kohmoto, K.: Ann. Phys.160, 343 (1985)

    Google Scholar 

  34. Chang, L. N., Liang, Y.: Mod. Phys. L A3, 1839 (1988)

    Google Scholar 

  35. Atiyah, M. F., Hitchin, N. J., Singer, I. M.: Proc. R. Soc. Lond. A362, 425 (1978)

    Google Scholar 

  36. Karoubi, M., Leruste, C.: Algebraic topology via differential geometry. Cambridge: Cambridge University Press 1987

    Google Scholar 

  37. Wu. Y. S., Zee, A.: Phys. Lett. B207, 39 (1988)

    Google Scholar 

  38. Chern, S.S., Simons, J.: Ann. Math.99, 48 (1974)

    Google Scholar 

  39. Moody, J., Shapere, A., Wilczek, F.: Phys. Rev. Lett.56, 893 (1986)

    Google Scholar 

  40. Tycko R.: Phys. Rev. Lett.58, 2281 (1987)

    Google Scholar 

  41. Segert, J.: Math. Phys.28, 2102 (1987)

    Google Scholar 

Download references

Author information

Author notes

  1. L. Sadun

    Present address: Courant Institute, New York University, 10012, NY, NY, USA

Authors and Affiliations

  1. Division of Physics, Mathematics and Astronomy, California Institute of Technology, 91125, Pasadena, CA, USA

    J. E. Avron, L. Sadun, J. Segert & B. Simon

Authors
  1. J. E. Avron
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. L. Sadun
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. Segert
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. B. Simon
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by A. Jaffe

On leave form Physics Dept., Technion, Haifa, 32000, Israel

Research partially supported by NSF Grant DMS-8801918

Rights and permissions

Reprints and permissions

About this article

Cite this article

Avron, J.E., Sadun, L., Segert, J. et al. Chern numbers, quaternions, and Berry's phases in Fermi systems. Commun.Math. Phys. 124, 595–627 (1989). https://doi.org/10.1007/BF01218452

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01218452

Keywords

Search

Navigation