Preview
Unable to display preview. Download preview PDF.
References
M.F. Atiyah, N.J. Hitchin, V.G. Drinfeld, Y.I. Manin, Phys. Lett. 65A, 185 (1978)
I.M. Singer, Proceedings of the International Congress of Mathematicians, Vancouver 1974. M. Kac, Amer. Math. Monthly 73, 1–23 (1966)
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)
S.W. Hawking, Comm. Math. Phys. 55, 133 (1977)
B.S. De Witt, Physics Reports 19C, 295 (1975) S.M. Christensen, Phys. Rev. D14, 2490 (1976); D17, 976 (1978)
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.
S. Coleman, unpublished J. Kiskis, Phys.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)
M.F. Atiyah, R. Bott, V.K. Patodi, Inventiones math. 19, 279 (1973)
N.K. Nielsen, Nordita preprint 78/24
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.
e.g. R.L. Bishop, R.J. Crittenden, “Geometry of Manifolds” Academic Press, New York and London 1964
N. Steenrod, “The Topology of Fibre Bundles”, Princeton University Press. D. Husemoller, “Fibre Bundles”, Springer New York, Heidelberg, Berlin.
J.W. Milnor, J.D. Stasheff, “Characteristic Classes”, Annals of Math. Studies Nr. 76 Princeton University Press
A.S. Schwarz, Phys. Lett. 67B, 172 (1977)
R. Jackiw, C. Rebbi, Phys. Lett. 67B, 189 (1977)
M. Atiyah, N. Hitchin, I.M. Singer, Proc. Nat. Acad. Sci. USA, 74, 2662 (1977); Proc. R. Soc. Lond. A362, 425 (1978)
C.W. Bernard, N.H., Christ, A.H. Gerth, E. Wienberg, Phys. Rev. D16, 2967 (1977)
H. Römer, Nuevo Cim. Lett 21. 381 (1978)
N.K. Nielsen, H. Römer, B. Schroer, Nucl. Phys. B136, 475 (1978)
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)
H. Römer, B. Schroer, Phys. Lett. 71B, 182 (1977)
T. Eguchi, P.B. Gilkey, A.J. Hanson, Phys. Rev. D17, 423 (1978) C.N. Pope, Nucl. Phys. B141, 432 (1978)
A.J. Hanson, H. Römer, Phys. Lett. 80B, 58 (1978) See e.g.
P.B. Gilkey, “Elliptic Operators on Compact Manifolds.”, Publish or Perish Inc. Boston 1974 and references herin.
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)
S.L. Adler, Phys. Rev. 177, 2426 (1969) J.S. Bell, R. Jackiw, Nuovo Cim. 60A, 47 (1969)
J.S. Dowker, J. of Phys. A11, 34 (1978)
M.T. Grisarn, P. van Nieuwenhuizen, D.Z. Friedemann, Phys. Lett. 71B, 377 (1978)
F. Hirzebruch, “Topological Methods in Algebraic Geometry”, Grundlagen der Math. Wissenschaften in Einzeldarstellungen Nr. 131, Springer N.Y. 1966.
R. Delbowgo, A. Salam, Phys. Lett. 30B, 381 (1972) T. Eguchi, P.G.O. Freund, Phys. Rev. Lett. 37, 1251 (1976)
See e.g. M. Greenberg, “Lectures on Algebraic Topology”, W.A. Benjamin, Inc., Amsterdam, New York 1967
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.
S.M. Christensen, M.J. Duff, Phys. Lett 76B, 571 (1978)
N.K. Nielsen, Nucl. Phys. B140, 499 (1978); B142, 306 (1978)
S.W. Hawking, Phys. Lett. 60A, 81 (1977)
T. Eguchi, A.J. Hanson, Phys. Lett. 74B, 249 (1978)
V.A. Belinskii, G. W. Gibbons, D.N. Page, C.N. Pope, Phys. Lett. 76B, 433 (1978)
N. Hitchin, Advances in Math. 14, 1 (1974)
M.F. Atiyah, unpublished
S.W. Hawking, C. N. Pope, Nucl. Phys. B146, 381 (1979)
G.W. Gibbons, C. N. Pope, H. Römer, Nucl. Phys. B157, 377 (1979)
N.K. Nielsen, Nucl. Phys. B151, 536 (1979)
H. Römer, Phys. Lett. 83B, 172 (1979)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1981 Springer-Verlag
About this paper
Cite this paper
Römer, H. (1981). Atiyah-Singer index theorem and quantum field theory. In: Doebner, HD. (eds) Differential Geometric Methods in Mathematical Physics. Lecture Notes in Physics, vol 139. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10578-6_29
Download citation
DOI: https://doi.org/10.1007/3-540-10578-6_29
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-10578-7
Online ISBN: 978-3-540-38573-8
eBook Packages: Springer Book Archive