Instantons in nonlinear σ-models, gauge theories and general relativity

  • Michael Forger
Gauge Theories
Part of the Lecture Notes in Physics book series (LNP, volume 139)


We consider nonlinear σ-models, gauge theories and general relativity as three classes of models of field theory which are of an intrinsically geometric nature as well as (possibly) topologically nontrivial, and explore the role of instantons as the basic tool for new perturbative schemes in these models. In particular, we emphasize the close analogy between nonlinear σ-models and pure gauge theories. We also establish a new, manifest type of analogy by extending them to “nonlinear σ-models with gauge symmetry” and “pure gauge theories in a frame field formulation”, respectively.


Gauge Theory Twistor Space Field Configuration Connection Form Christoffel Symbol 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1).
    M.F. Atiyah, R.S. Ward: Commun. Math. Phys. 55, 117 (1977)Google Scholar
  2. 2).
    M.F. Atiyah, Q.J. Hitchin, I.M. Singer: Proc. Roy. Soc. London 362, 425 (1978)Google Scholar
  3. 3).
    M. Atiyah, V.G. Drinfeld, N.J. Hitchin, Yu.I. Manin: Phys. Lett. 65A, 185 (1978)Google Scholar
  4. 4).
    A. Back, M. Forger, P.G.O. Freund: Phys. Lett. 77B, 181 (1978)Google Scholar
  5. 5).
    A.A. Belavin, A.M. Polyakov, A.S. Schwarz, Y.S. Tyupkin: Phys. Lett. 59B, 85 (1975)Google Scholar
  6. 6).
    S. Coleman: “The Uses of Instantons”, in: Proc. 1977 Summer School Subnuclear Phys., EriceGoogle Scholar
  7. 7).
    A. D'Adda, P. Di Vecchia, M. Lüscher: Nucl. Phys. B146, 63 (1978)Google Scholar
  8. 8).
    J. Eells, J.H. Sampson: Am. J. Math 86, 109 (1964)Google Scholar
  9. 9).
    J. Eells, L. Lemaire: Bull. London Math. Soc. 10, 1 (1978)Google Scholar
  10. 10).
    T. Eguchi, A. Hanson: Phys. Lett. 74B, 249 (1978)Google Scholar
  11. 11).
    H. Eichenherr: Nucl. Phys. B146, 215 (1978)Google Scholar
  12. 12).
    L.D. Fadeev, V.N. Popov: Phys. Lett. 25B, 29 (1967)Google Scholar
  13. 13).
    R.P. Feynman: Phys. Rev. 80, 440 (1950)Google Scholar
  14. 14).
    R.P. Feynman, A.R. Hibbs: “Quantum Mechanics and Path Integrals”, Mc Graw-Hill, New York (1965)Google Scholar
  15. 15).
    H. Flanders: “Differential Forms”, Academic Press, New York (1963)Google Scholar
  16. 16).
    M. Forger: “Gauge Theories, Instantons and Algebraic Geometry”, in: Proc.. Diff. Geom. Math. Phys., Clausthal-Zellerfeld (1977); to appear in Rep. Math. Phys.Google Scholar
  17. 17).
    G.W. Gibbons, S.W. Hawking: Phys. Rev. D15. 2752 (1977)Google Scholar
  18. 18).
    G.W. Gibbons, S.W. Hawking: Phys. Lett. 78B, 430 (1978)Google Scholar
  19. 19).
    G.W. Gibbons, S.W. Hawking, M.J. Perry: Nucl. Phys. B138, 141 (1978)Google Scholar
  20. 20).
    G.W. Gibbons, M.J. Perry: Nucl. Phys. B146, 90 (1978)Google Scholar
  21. 21).
    G.W. Gibbons, C.N. Pope: Commun. Math. Phys. 61, 239 (1978)Google Scholar
  22. 22).
    V.L. Golo, A. M. Perelomov: Lett. Math. Phys. 2, 477 (1978)Google Scholar
  23. 23).
    W. Greub, S. Halperin, R. Vanstone: “Connections, Curvature and Cohomology”, Vol. I (1972) and Vol. II (1973), Academic Press, New YorkGoogle Scholar
  24. 24).
    S.W. Hawking: “Spacetime Foam”, DAMTP preprint, Cambridge, UK (1978)Google Scholar
  25. 25).
    S.W. Hawking: Phys. Rev. D18, 1747 (1978)Google Scholar
  26. 26).
    F. Hirzebruch: “Topological Methods in Algebraic Geometry”, 3rd edition, Springer, New York (1966)Google Scholar
  27. 27).
    H. Hogreve, R. Schrader, R. Seiler: Nucl. Phys. B142, 525 (1978)Google Scholar
  28. 28).
    D. Husemoller: “Fibre Bundles”, 2nd edition, Springer, Berlin (1966)Google Scholar
  29. 29).
    A. Lichnerowicz: “Applications harmoniques et variétés kähleriennes”, in: Symp. Math. Bologna III, Academic Press, New York (1970)Google Scholar
  30. 30).
    Y. Nambu: “The Confinement of Quarks”, in: Scientific American 235, 48 (Nov. 1976)Google Scholar
  31. 31).
    M.S. Narasimhan, S. Ramanan: Am. J. Math. 83, 563 (1961)Google Scholar
  32. 32).
    E. Nelson: “Tensor Analysis”, Princeton University Press, Princeton (1967)Google Scholar
  33. 33).
    A.M. Perelomov: Commun. Math. Phys. 63, 237 (1978)Google Scholar
  34. 34).
    V.N. Popov: “Functional Integrals in Quantum Field Theory”, CERN preprint TH 2424 (Dec. 1977)Google Scholar
  35. 35).
    N. Steenrod: “The Topology of Fibre Bundles”, Princeton University Press, Princeton (1951)Google Scholar
  36. 36).
    R. Stora: “Yang-Mills Instantons, Geometrical Aspects”, in: Proc. 1977Google Scholar
  37. 37).
    Summer School Mathematical Phys., Erice, Lecture Notes in Physics, Vol. 73, Springer, Berlin (1978)Google Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Michael Forger
    • 1
  1. 1.Institut für theoretische PhysikFreie Universität BerlinBerlin 33Germany

Personalised recommendations