Skip to main content
SpringerLink
Log in
Book cover

Non-linear Partial Differential Operators and Quantization Procedures pp 142–169Cite as

The twistor-geometric representation of classical field theories

  • Part I Non-linear Partial Differential Operators
  • Conference paper
  • First Online:

  • 443 Accesses

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1037))

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   46.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Atiyah, M.F., Geometry of Yang-Mills Fields, Lezioni Ferminone, Acad. Naz. dei Lincei Scuola Normal Sup., Pisa, 1979.

    Google Scholar 

  2. Atiyah, M.F., "Green's functions for self-dual 4-manifolds", Math. Analysis and Applications, Part A, Adv. in Math., Suppl. Stnd., 7a, Acad. Press, New York, pp 129–158, 1981.

    Google Scholar 

  3. Atiyah, M.F., Hitchin, N.J., and Singer, I., "Self-duality in four-dimensional Riemannian geometry", Proc. Roy. Soc. Lond. A 362 (1978), 425–461.

    Article  MathSciNet  MATH  Google Scholar 

  4. Atiyah, M.F., and Ward, R., "Instantons and algebraic geometry", Comm. Math. Phys. 55 (1977), 111–124.

    Article  MathSciNet  Google Scholar 

  5. Atiyah, M.F., Hitchin, N.J., Dringeld, V.G., and Manin, Yu.I., "Construction of instantons", Phys. Lett. 65A (1978), 185–187

    Google Scholar 

  6. Bailey, Toby, Ehrenpreis, L., and Wells, R.O., Jr., "Removeable singularities for massless fields", (in preparation, 1982).

    Google Scholar 

  7. Bjorken, J.D., and Drell, S.D., Relativistic Quantum Fields, McGraw-Hill, New York, 1965.

    MATH  Google Scholar 

  8. Curtis, W.D., D.E. Lerner, and F.R. Miller, "Complex PP-waves and the nonlinear graviton construction", J. Math. Phys., (1978), 2024–2027.

    Google Scholar 

  9. Eastwood, M.G., "On the twistor description of massive fields", Proc. R. Soc. Lond. A 374 (1981), 413–445.

    MathSciNet  Google Scholar 

  10. Eastwood, M.G., R. Penrose, and R.O. Wells, Jr., "Cohomology and massless fields", Comm. Math. Phys., 78 (1981), 305–351.

    Article  MathSciNet  MATH  Google Scholar 

  11. Ernst, F.J., Phys. Rev. 167 (1968), 1175.

    Article  Google Scholar 

  12. Gindikhin, S.G., "Twistor representation of the solutions of Maxwell's system", (Russian), Funkcional. Anal. i Prilozen. 14 (1980), 64–66.

    Google Scholar 

  13. Gindikhin, S. and G. Henkin, "Complex integral geometry and the Penrose representation of solutions of Maxwell's equations", (Russian) Teor. i Math. Phys., 43 (1980), 18–31.

    Google Scholar 

  14. Hawking, S.W., and G.F.R. Ellis, The large scale structure of space-time, Cambridge Univ. Press, Cambridge, 1973.

    Book  MATH  Google Scholar 

  15. Helgason, S., The Radon Transform, Birkhäuer, Boston, 1980.

    MATH  Google Scholar 

  16. Henkin, G.M., and Yu.I. Manin, "Twistor description of classical Yang-Mills-Dirac fields", Phys. Lett. 95B (1980), 405–409.

    MathSciNet  Google Scholar 

  17. Hitchin, N.J., "Polygons and gravitons", Math. Proc. Camb. Phil. Soc., 85 (1979), 465–476.

    Article  MathSciNet  Google Scholar 

  18. Hughston, L.P., and T.R. Hurd, "A cohomological description of massive fields", (Oxford preprint, 1981).

    Google Scholar 

  19. Infeld, L., and B.L. van der Waerden, "Die Wellengleichung des Elektrons in der allgemeinen Relativitätstheorie", Sitz.-Ber. preuss. Akad. Wiss. 9 (1933), 380–401.

    Google Scholar 

  20. Isenberg, J., P.B. Yasskin, and P.S. Green, "Non-self-dual gauge fields", Phys. Lett. 78B (1978), 462–464.

    Google Scholar 

  21. Klein, F., "Einleitung in die Höhere Geometrie, Göttingen, (1883).

    Google Scholar 

  22. Kuiper, N., "On conformally flat spaces in the large", Ann. of Math. 50 (1949), 916–924.

    Article  MathSciNet  MATH  Google Scholar 

  23. LeBrun, Claude, "The first formal Neighbourhood of ambitwistor space for curved space-time", Lett.in Math.Phys. 6 (1982), 345–354

    Article  MathSciNet  MATH  Google Scholar 

  24. Manton, N.S., Nucl. Phys. B135, (1978), 319–332.

    Article  Google Scholar 

  25. Newman, E.T., "Deformed twistor space and H-space", Complex Manifold Technique in Theoretical Physics (eds: D.E. Lerner and P.D. sommers), Pitman, San Francisco-London-Melbourne, (1979), pp. 154–165.

    Google Scholar 

  26. Patton, C.M., "On representation in cohomology over pseudohermitian symmetric spaces", Bull. Amer. Math. Soc. (NS) 5 (1981), 63–66.

    Article  MathSciNet  MATH  Google Scholar 

  27. Penrose, Roger, "The light cone at infinity", Proceedings of the 1962 Conference on relativistic theories of gravitation, Warsaw, Polish Acad. of Sci., 1965, pp 369–373.

    Google Scholar 

  28. Penrose, Roger, "Twistor algebra", J. Math. Phys. 8 (1967), 345–366.

    Article  MathSciNet  MATH  Google Scholar 

  29. Penrose, Roger, "Twistor quantisation and curved space-time", J. of Theor. Phys. 1 (1968), 61–99.

    Article  Google Scholar 

  30. Penrose, Roger, "Solutions of the zero-rest-mass equations", J. Math. Phys. 10 (1969), 38–39.

    Article  MathSciNet  Google Scholar 

  31. Penrose, Roger, and McCallum, M.A.H., "Twistor theory: an approach to the quantization of fields and space-time", Phys. Rep. 6C (1972), 241–316.

    Google Scholar 

  32. Penrose, Roger, "Nonlinear gravitons and curved twistor theory", General Rel. and Grav. 7 (1976), 31–52.

    Article  MathSciNet  MATH  Google Scholar 

  33. Pool, Robert, "Yang-Mills fields and extension theory", Memoirs Amer. Math. Soc. (1982), (to appear).

    Google Scholar 

  34. Rawnslay, J., W. Schmid, and J.A. Wolf, "Singuler unitary representations and indefinite harmonic theory" (1982 preprint).

    Google Scholar 

  35. Segal, I.E., Mathematical Cosmology and Extragalactic Astronomy, Academic Press, New York, 1976.

    Google Scholar 

  36. Ward, R., "On self-dual gauge fields", Phys. Lett. 61A (1977), 81–82.

    Google Scholar 

  37. Ward, R., "A class of self-dual solutions of Einstein's equations", Proc. R. Soc. Lond. A, 363 (1978), 289–295.

    Article  MATH  Google Scholar 

  38. Ward, R., "A Yang-Mills-Higgs monopole of charge 2", Comm. Math. Phys. 79 (1981), 317–325.

    Article  MathSciNet  Google Scholar 

  39. Wells, R.O., Jr., "Complex manifolds and mathematical physics", Bull. Amer. Math. Soc. (NS), 1 (1979), 296–336.

    Article  MATH  Google Scholar 

  40. Wells, R.O., Jr., Differential Analysis on Complex Manifolds", Springer-Verlag, New York-Heidelberg-Berlin, 1980.

    Book  MATH  Google Scholar 

  41. Wells, R.O., Jr., "Hyperfunction solutions of the zero-restmass field equations", Comm. Math. Phys. 78 (1981), 567–600.

    Article  MATH  Google Scholar 

  42. Wells, R.O., Jr., "The conformally invariant Laplacian and the instanton vanishing theorem", Seminar on Differential Geometry (ed: S.T. Yau), Ann. of Math. Studies (in print), (1982), (a), Princeton Uni. Press, Princeton NT, 483–498.

    Google Scholar 

  43. Wells, R.O., Jr., "Complex Geometry in Mathematical Physics", Univ. of Montreal Press, (1982).

    Google Scholar 

  44. Witten, E., "An interpretation of classical Yang-Mills theory", Phys. Lett. 77B (1978), 394–398.

    Google Scholar 

  45. Witten, L., "Static axially symmetric solutions of self-dual SU(2) gauge fields in Euclidean four-dimensional space", Phys. Rev. D19 (1979), 718–720.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Rice University, 77251, Houston, TX, USA

    R. O. Wells Jr.

Authors
  1. R. O. Wells Jr.
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institut für Theoretische Physik, Technische Universität Clausthal, 3392, Clausthal-Zellerfeld, Federal Republic of Germany

    Stig I. Andersson  & Heinz-Dietrich Doebner  & 

Rights and permissions

Reprints and permissions

Copyright information

© 1983 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Wells, R.O. (1983). The twistor-geometric representation of classical field theories. In: Andersson, S.I., Doebner, HD. (eds) Non-linear Partial Differential Operators and Quantization Procedures. Lecture Notes in Mathematics, vol 1037. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073172

Download citation

  • DOI: https://doi.org/10.1007/BFb0073172

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12710-9

  • Online ISBN: 978-3-540-38695-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation