Chern numbers, quaternions, and Berry's phases in Fermi systems
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Abstract
Yes, but some parts are reasonably concrete.
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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 1982Google Scholar
- 9.Kobayashi, S., Nomizu, K.: Foundations of differential geometry, vol. I and II. New York: John Wiley 1963, 1969Google Scholar
- 10.Atiyah, M.F.: Geometry of Yang-Mills fields, Lezioni Fermiane. Pisa: Accademia Nazionale dei Lincei & Scuola Normale Superiore 1979Google Scholar
- 11.Chern, S. S.: Complex manifolds without potential theory, sec. ed. Berlin, Heidelberg, New York: Springer 1979Google Scholar
- 12.Zee, A.: Phys. Rev. A38, 1 (1988)Google Scholar
- 13.Tinkham, M.: Group theory and quantum mechanics. New York: McGraw-Hill 1964Google Scholar
- 14.Bjorken, J. D., Drell, S. D.: Relativistic quantum mechanics. New York: McGraw-Hill 1964;Google Scholar
- 14a.Itzykson, C., Zuber, J. B.: Quantum field theory. New York: McGraw-Hill 1980Google Scholar
- 15.Wigner, E. P.: Göttinger Nachr.31, 546 (1932); Wigner, E. P.: Group Theory. New York: Academic Press 1959Google Scholar
- 16.Frobenius, Schur: Berl. Ber., p. 186 (1906)Google Scholar
- 17.Dyson, F.: J. Math. Phys.3, 140 (1964)Google Scholar
- 18.Mehta, M. L.: Random matrices and the statistical theory of energy levels. New York: Academic Press 1967Google Scholar
- 19.Kramers, H.A.: Proc. Acad. Amsterdam33, 959 (1930)Google Scholar
- 20.Adams, J.F.: Lectures on Lie Groups. Chicago: University of Chicago Press 1969Google Scholar
- 21.Bröcker, T., tom Dieck, T.: Representations of compact Lie groups. Berlin, Heidelberg, New York: Springer 1985Google Scholar
- 22.Sadun, L., Segert, J.: J. Phys. A22, L 111 (1989)Google Scholar
- 23.von Neumann, J., Wigner, E.P.: Phys. Zeit.30, 467 (1929)Google Scholar
- 24.Friedland, S., Robbin, J. W., Sylvester, J. H.: On the crossing rule. Commun. Pure Appl. Math.37, 19 (1984)Google Scholar
- 25.Mermin, N. D.: Rev. Mod. Phys.51, No. 3 (1979)Google Scholar
- 26.Avron, J., Seiler, R., Simon, B.: Phys. Rev. Lett.51, 51 (1983)Google Scholar
- 27.Steenrod, N.: The topology of fibre bundles. Princeton: Princeton University Press 1951Google Scholar
- 28.Bott, R., Tu, L. W.: Differential forms in algebraic topology. Berlin, Heidelberg, New York: Springer 1982Google Scholar
- 29.Herzberg, G., Longuet-Higgins, H. C.: Discuss. Faraday Soc.55, 77 (1963)Google Scholar
- 30.Milnor, J. W., Stasheff, J. D.: Characteristic classes. Princeton, NJ: Princeton University Press 1974Google Scholar
- 31.Thouless D., et. al.: Phys. Rev. Lett.49, 405 (1982)Google Scholar
- 32.Kohmoto, K.: Ann. Phys.160, 343 (1985)Google Scholar
- 33.Chang, L. N., Liang, Y.: Mod. Phys. L A3, 1839 (1988)Google Scholar
- 34.Atiyah, M. F., Hitchin, N. J., Singer, I. M.: Proc. R. Soc. Lond. A362, 425 (1978)Google Scholar
- 35.Karoubi, M., Leruste, C.: Algebraic topology via differential geometry. Cambridge: Cambridge University Press 1987Google Scholar
- 36.Wu. Y. S., Zee, A.: Phys. Lett. B207, 39 (1988)Google Scholar
- 37.Chern, S.S., Simons, J.: Ann. Math.99, 48 (1974)Google Scholar
- 38.Moody, J., Shapere, A., Wilczek, F.: Phys. Rev. Lett.56, 893 (1986)Google Scholar
- 39.Tycko R.: Phys. Rev. Lett.58, 2281 (1987)Google Scholar
- 40.Segert, J.: Math. Phys.28, 2102 (1987)Google Scholar
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