Skip to main content

Twistor Theory (The Penrose Transform)

  • Conference paper
  • 887 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 950)

Abstract

Where does complex mathematics intervene in our real world? [5]

Answer: Twistor Theory! [19]

Twistors were introduced by Penrose [11, 13] in order to provide an alternative description of Minkowski-space which emphasizes the light rays rather than the points of space-time. Minkowski-space constructions must be replaced by corresponding constructions in twistor-space. The twistor programme [17] has met with much success:

  1. (1)

    The description of massless free fields (the Penrose transform)

  2. (2)

    The description of self-dual Einstein manifolds

  3. (3)

    The description of self-dual Yang-Mills fields

  4. (4)

    The description of elementary particles (rather tentative).

Keywords

  • Complex Manifold
  • Real Hypersurface
  • Twistor Theory
  • Pitman Research Note
  • Massless Field

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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   44.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   59.00
Price excludes VAT (Canada)
  • 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. M.F. Atiyah, N.J. Hitchin, V.G. Dinfeld, Yu.I. Manin: Construction of instantons, Phys. Lett. 65A, 185–187 (1978).

    Google Scholar 

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

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. M.G. Eastwood: On the twistor description of massive fields, Proc. Roy. Soc. Lond. A 374, 431–445 (1981).

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. M.G. Eastwood and M.L. Ginsberg: Duality in twistor theory, Duke Math. J. 48 (1981).

    Google Scholar 

  5. J. Eells: Complex analysis and geometry, lecture notes, this seminar.

    Google Scholar 

  6. M.L. Ginsberg, S.A. Huggett: Sheaf cohomology and twister diagrams, in [10], 287–292.

    Google Scholar 

  7. M.L. Ginsberg: A cohomological scalar product construction, in [10], 293–300.

    Google Scholar 

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

    CrossRef  MathSciNet  Google Scholar 

  9. L.P. Hughston: Twistors and particles, Springer lecture notes in physics 97 (1979).

    Google Scholar 

  10. L.P. Hughston, R.S. Ward (eds.); Advances in twistor theory, Pitman research notes in math. 37 (1979).

    Google Scholar 

  11. R. Penrose: Twistor algebra, J. Math. Phys. 8, 345–366 (1967).

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. R. Penrose: The structure of space-time, in Batelle rencontres, eds. C.M. DeWitt, J.A. Wheeler, 121–235, Benjamin (1967).

    Google Scholar 

  13. R. Penrose; Twistor quantization and curved space-time, Int. J. Th. Phys. 1, 61–99 (1968).

    CrossRef  Google Scholar 

  14. R. Penrose: Twistor theory, it aims and achievements, in Quantum gravity, an Oxford symposium, eds C.J. Isham, R. Penrose, D.W. Sciama, 268–407, Oxford Clarendon Press (1975).

    Google Scholar 

  15. R. Penrose: Twistors and particles — an outline, in Quantum theory and the structure of space-time, eds. L. Castell, M. Drieschner, C.F. von Weizsacker, 129–145, Carl Hanser Verlag (1975).

    Google Scholar 

  16. R. Penrose, Non-linear gravitons and curved twistor theory, Gen. Rel. Grav. 7, 31–52 (1976).

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. R. Penrose: The twistor programme, Reps. on Math. Phys. 12, 65–76 (1977).

    CrossRef  MathSciNet  Google Scholar 

  18. R. Penrose: On the twistor description of massless fields, in Complex manifold technqiues in theoretical physics, eds. D.E. Lerner, P.O. Sommers, 55–91, Pitman research notes in math. 32 (1979).

    Google Scholar 

  19. R. Penrose: Is nature complex?, in the Encyclopedia of ignorance, eds. R. Duncan, M. Weston-Smith, Pergamon (1977).

    Google Scholar 

  20. R. Penrose, R.S. Ward: Twistors for flat and curved space-time, in Einstein centennial volume, ed. A.P. Held, Plenum (1980).

    Google Scholar 

  21. G. Trautman: Holomorphic vector-bundles and Yang-Mills fields, lecture notes, this seminar.

    Google Scholar 

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

    Google Scholar 

  23. R.O. Wells, Jr.: Complex manifolds and mathematical physics, Bull. Amer. Math. Soc. 1, (new series), 296–336 (1979).

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 1982 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Eastwood, M.G. (1982). Twistor Theory (The Penrose Transform). In: Complex Analysis. Lecture Notes in Mathematics, vol 950. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0061875

Download citation

  • DOI: https://doi.org/10.1007/BFb0061875

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11596-0

  • Online ISBN: 978-3-540-39366-5

  • eBook Packages: Springer Book Archive