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Atiyah-Singer index theorem and quantum field theory

  • H. Römer
3. Elliptic Operators, Spectral Theory and Physical Applications
Part of the Lecture Notes in Physics book series (LNP, volume 139)

Keywords

Vector Bundle Dirac Operator Elliptic Operator Index Theorem Lens Space 
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References

  1. 1).
    M.F. Atiyah, N.J. Hitchin, V.G. Drinfeld, Y.I. Manin, Phys. Lett. 65A, 185 (1978)Google Scholar
  2. 2).
    I.M. Singer, Proceedings of the International Congress of Mathematicians, Vancouver 1974. M. Kac, Amer. Math. Monthly 73, 1–23 (1966)Google Scholar
  3. 3).
    H.B. G. Casimir, Proc. Kon. Ned. Akad. Wetenschap 51, 793 (1948), see also T.H. Boyer, Ann. Phys. (N.Y.) 56, 474 (1979) and ref. 5)Google Scholar
  4. 4).
    S.W. Hawking, Comm. Math. Phys. 55, 133 (1977)Google Scholar
  5. 5).
    B.S. De Witt, Physics Reports 19C, 295 (1975) S.M. Christensen, Phys. Rev. D14, 2490 (1976); D17, 976 (1978)Google Scholar
  6. 6).
    M.F. Atiyah, I.M. Singer, Bull. Amer. Math. Soc. 69, 422 (1969) Amer. Math. 87, 484 and 546 (1968) M.F. Atiyah, G.B. Segal, Ann. Math. 87, 530 (1968) R. Palais ed. “Seminar on the Atiyah-Singer Index Theorem” Annals of Math. Studies 57, Princeton University Press.Google Scholar
  7. 7).
    S. Coleman, unpublished J. Kiskis, Phys. Rev. D15, 2329 (1977) R. Jackiw, C. Rebbi, Phys. Rev. D16, 1052 (1977) N.K. Nielsen, B. Schroer, Nuclear Phys. B 127, 493 (1977) N.K. Nielsen, H. Römer, B. Schroer, Phys. Lett. 70B, 445 (1977)Google Scholar
  8. 8).
    M.F. Atiyah, R. Bott, V.K. Patodi, Inventiones math. 19, 279 (1973)Google Scholar
  9. 9).
    N.K. Nielsen, Nordita preprint 78/24Google Scholar
  10. 10).
    M.T. Grisarn, N.K. Nielsen, H. Römer, P. van Niewenhuizen, Nucl. Phys. B140 477 (1978), N.K. Nielsen and H. Römer, Proc. Informal Meeting on recent developments in field theory Nov 1977 ICTP/77/152, pp. 27–28.Google Scholar
  11. 11).
    e.g. R.L. Bishop, R.J. Crittenden, “Geometry of Manifolds” Academic Press, New York and London 1964Google Scholar
  12. 12).
    N. Steenrod, “The Topology of Fibre Bundles”, Princeton University Press. D. Husemoller, “Fibre Bundles”, Springer New York, Heidelberg, Berlin.Google Scholar
  13. 13).
    J.W. Milnor, J.D. Stasheff, “Characteristic Classes”, Annals of Math. Studies Nr. 76 Princeton University PressGoogle Scholar
  14. 14).
    A.S. Schwarz, Phys. Lett. 67B, 172 (1977)Google Scholar
  15. 15).
    R. Jackiw, C. Rebbi, Phys. Lett. 67B, 189 (1977)Google Scholar
  16. 16).
    M. Atiyah, N. Hitchin, I.M. Singer, Proc. Nat. Acad. Sci. USA, 74, 2662 (1977); Proc. R. Soc. Lond. A362, 425 (1978)Google Scholar
  17. 17).
    C.W. Bernard, N.H., Christ, A.H. Gerth, E. Wienberg, Phys. Rev. D16, 2967 (1977)Google Scholar
  18. 18).
    H. Römer, Nuevo Cim. Lett 21. 381 (1978)Google Scholar
  19. 19).
    N.K. Nielsen, H. Römer, B. Schroer, Nucl. Phys. B136, 475 (1978)Google Scholar
  20. 20).
    M.F. Atiyah, V.K. Patodi, I.M. Singer, Bull. Londons Math. Soc 5, 229 (1973), Math. Proc. Cambridge Philos. Soc. 77, 43 (1975); 78, 405 (1975); 79, 71 (1976)Google Scholar
  21. 21).
    H. Römer, B. Schroer, Phys. Lett. 71B, 182 (1977)Google Scholar
  22. 22).
    T. Eguchi, P.B. Gilkey, A.J. Hanson, Phys. Rev. D17, 423 (1978) C.N. Pope, Nucl. Phys. B141, 432 (1978)Google Scholar
  23. 23).
    A.J. Hanson, H. Römer, Phys. Lett. 80B, 58 (1978) See e.g.Google Scholar
  24. 24).
    P.B. Gilkey, “Elliptic Operators on Compact Manifolds.”, Publish or Perish Inc. Boston 1974 and references herin.Google Scholar
  25. 25).
    See e.g. S. Chern, J. Simons, Proc. Nat. Acad. Sci. (USA) 68, 791 (1971); Ann. of Math. (2) 99, 48 (1974) and Milnor, Stasheff, ref. 13)Google Scholar
  26. 26).
    S.L. Adler, Phys. Rev. 177, 2426 (1969) J.S. Bell, R. Jackiw, Nuovo Cim. 60A, 47 (1969)Google Scholar
  27. 27).
    J.S. Dowker, J. of Phys. A11, 34 (1978)Google Scholar
  28. 28).
    M.T. Grisarn, P. van Nieuwenhuizen, D.Z. Friedemann, Phys. Lett. 71B, 377 (1978)Google Scholar
  29. 29).
    F. Hirzebruch, “Topological Methods in Algebraic Geometry”, Grundlagen der Math. Wissenschaften in Einzeldarstellungen Nr. 131, Springer N.Y. 1966.Google Scholar
  30. 30).
    R. Delbowgo, A. Salam, Phys. Lett. 30B, 381 (1972) T. Eguchi, P.G.O. Freund, Phys. Rev. Lett. 37, 1251 (1976)Google Scholar
  31. 31).
    See e.g. M. Greenberg, “Lectures on Algebraic Topology”, W.A. Benjamin, Inc., Amsterdam, New York 1967Google Scholar
  32. 32).
    S. Deser, B. Zumino, Phys. Lett. 62B, 335 (1976) For a review see e.g. S. Ferrara, Erice Lectures Aug. 1978) CERN TH 2514, an almost complete list of references is contained in “Proceedings of the Supergravity Workshop at Stony Brook, 27.–29. Sept. 1979, P. van Nieuwenhuizen, D.Z. Friedman eds.Google Scholar
  33. 33).
    S.M. Christensen, M.J. Duff, Phys. Lett 76B, 571 (1978)Google Scholar
  34. 34).
    N.K. Nielsen, Nucl. Phys. B140, 499 (1978); B142, 306 (1978)Google Scholar
  35. 35).
    S.W. Hawking, Phys. Lett. 60A, 81 (1977)Google Scholar
  36. 36).
    T. Eguchi, A.J. Hanson, Phys. Lett. 74B, 249 (1978)Google Scholar
  37. 37).
    V.A. Belinskii, G. W. Gibbons, D.N. Page, C.N. Pope, Phys. Lett. 76B, 433 (1978)Google Scholar
  38. 38).
    N. Hitchin, Advances in Math. 14, 1 (1974)Google Scholar
  39. 39).
    M.F. Atiyah, unpublishedGoogle Scholar
  40. 40).
    S.W. Hawking, C. N. Pope, Nucl. Phys. B146, 381 (1979)Google Scholar
  41. 41).
    G.W. Gibbons, C. N. Pope, H. Römer, Nucl. Phys. B157, 377 (1979)Google Scholar
  42. 42).
    N.K. Nielsen, Nucl. Phys. B151, 536 (1979)Google Scholar
  43. 43).
    H. Römer, Phys. Lett. 83B, 172 (1979)Google Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • H. Römer
    • 1
  1. 1.Fakultät für PhysikUniversität FreiburgFreiburg

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