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Cohomology and massless fields

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References

  1. Andreotti, A., Grauert, H.: Théorèmes de finitude pour cohomologie des espaces complexes. Bull. Soc. Math. France90, 193–259 (1962)

    Google Scholar 

  2. Atiyah, M. F., Hitchin, N. J., Drinfeld, V. G., Manin, Yu. I.: Construction of instantons. Phys. Lett.65A, 185–187 (1978)

    Google Scholar 

  3. Atiyah, M. F., Ward, R.: Instantons and algebraic geometry. Commun. Math. Phys.55, 111–124 (1977)

    Google Scholar 

  4. Bateman, H.: The solution of partial differential equations by means of definite integrals. Proc. London Math. Soc. (2)1, 451–458 (1904)

    Google Scholar 

  5. Bredon, G. E.: Sheaf theory. New York, St. Louis, San Francisco, Toronto, London, Sydney: McGraw-Hill 1967

    Google Scholar 

  6. Dirac, P. A. M.: Relativistic wave equations. Proc. R. Soc. London Ser. A155, 447–459 (1936)

    Google Scholar 

  7. Drinfeld, V. G., Manin, Yu. I.: Instantons and sheaves on ℂℙ3. Functional Anal. Appl.13, 59–74 (1979), (Engl. trans. 124–134 (1979))

    Google Scholar 

  8. Eastwood, M. G.: Some cohomological arguments applicable to twistor theory. Twistor Newsletter7, 6–10 (1978)

    Google Scholar 

  9. Eastwood, M. G.: Zero-rest-mass fields and topology. Twistor Newsletter7, 11–11 (1978)

    Google Scholar 

  10. Eastwood, M. G.: On raising and lowering helicity. Twistor Newsletter8, 37–38 (1979)

    Google Scholar 

  11. Eastwood, M. G.: Ambitwistors. Twistor Newsletter9, 55–58 (1979)

    Google Scholar 

  12. Fierz, M.: Über die relativistische Theorie kräftefreier Teilchen mit beliebigem Spin. Helv. Phys. Acta12, 3–37 (1939)

    Google Scholar 

  13. Gasiorowicz, S.: Elementary particle physics. New York: Wiley 1966

    Google Scholar 

  14. Godement R.: Topologie algébrique et théorie des faisceaux. Paris: Hermann 1964

    Google Scholar 

  15. Gindikhin, S., Henkin, G.: Integral geometry for\(\overline \partial \)-cohomology in q-linearly concave domains in ℂℙn (Russian). Functional Anal. Appl.12 6–23 (1978) (Engl. Trans. 247–261 (1979)

    Google Scholar 

  16. Grgin, E.: A global technique for the study of spinor fields. Ph.D. Thesis, Department of Physics, Syracuse University 1966

  17. Griffiths, P., Adams, J.: Topics in algebraic and analytic geometry. In: Math. Notes 13. Princeton: Princeton University Press 1974

    Google Scholar 

  18. Grothendieck, A.: Sur la classification des fibrés holomorphes sur la sphère de Riemann. Am. J. Math.79, 121–138 (1957)

    Google Scholar 

  19. Gunning, R. C., Rossi, H.: Analytic functions of several complex variables. Englewood Cliffs, N. J.: Prentice-Hall 1965

    Google Scholar 

  20. Hitchin, N. J.: Linear field equations on self-dual spaces. Proc. R. Soc. London Ser-A370, 173–191 (1980)

    Google Scholar 

  21. Hörmander, L.: An introduction to complex analysis in several variables. Amsterdam: North-Holland 1973

    Google Scholar 

  22. Hughston, L. P.: The twistor cohomology of local Hertz potentials. Twistor Newsletter4, 12–16 (1977)

    Google Scholar 

  23. Hughston, L. P.: Some new contour integral formulae. In: Complex manifold techniques in theoretical physics (eds. D. E. Lerner, P. D. Sommers). Research Notes in Math.32, 115–125. San Fransisco, London, Melbourne: Pitman 1979

    Google Scholar 

  24. Hughston, L. P.: Twistors and particles. In: Lecture Notes in Physics 97. Berlin, Heidelberg, New York: Springer 1979

    Google Scholar 

  25. Lerner, D. E.: The “inverse twistor function” for positive frequency fields. Twistor Newsletter5, 17–18 (1977)

    Google Scholar 

  26. Lerner, D. E.: Twistors and induced representations of SU(2, 2). J. Math. Phys. (N.Y.)18, 1812–1817 (1977)

    Google Scholar 

  27. Malgrange, B.: Faisceaux sur des variétés analytiques-réelles. Bull. Soc. Math. France85, 231–237 (1957)

    Google Scholar 

  28. Milnor, J., Stasheff, J.: Characteristic classes. Princeton: Princeton University Press 1974

    Google Scholar 

  29. Penrose, R.: Zero-rest-mass fields including gravitation: asymptotic behaviour. Proc. R. Soc. London Ser. A284, 159–203 (1965)

    Google Scholar 

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

    Google Scholar 

  31. Penrose, R.: Solutions of the zero-rest-mass equations. J. Math. Phys. (N.Y.)10, 38–39 (1969)

    Google Scholar 

  32. Penrose, R.: Twistor quantization and curved space-time. Int. J. Theor. Phys.1, 61–99 (1968)

    Google Scholar 

  33. Penrose, R.: The structure of space-time. In: Battelle rencontres 1967, pp. 121–235. New York: Benjamin 1968

    Google Scholar 

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

    Google Scholar 

  35. Penrose, R.: Twistor theory, its aims and achievements. In: Quantum gravity: an Oxford Symposium (eds. C. J. Isham, R. Penrose, D. W. Sciama, pp. 268–407. Oxford: Clarendon Press 1975

    Google Scholar 

  36. Penrose, R.: Twistors and particles: an outline. In: Quantum theory and the structure of spacetime (eds. L. Castell, M. Drieschner, C. F. von Weizsäcker,) Munich: Munich Verlag 1975

    Google Scholar 

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

    Google Scholar 

  38. Penrose, R.: Twistor functions and sheaf cohomology. Twistor Newsletter2, 3–12 (1976)

    Google Scholar 

  39. Penrose, R.: Massless fields and sheaf cohomology. Twistor Newsletter5, 9–13 (1977)

    Google Scholar 

  40. Penrose, R.: The twistor programme. Rep. Mathematical Phys.12, 65–76 (1977)

    Google Scholar 

  41. Penrose, R.: Twistors as helicity raising operators. Twistor Newsletter8, 35–36 (1979)

    Google Scholar 

  42. Penrose, R., Rindler, W.: Spinors and space-time structure. Cambridge: Cambridge University Press (to appear)

  43. Penrose, R., Ward, R. S.: Twistors for flat and curved space-time. Einstein centennial volume (eds. P. G. Bergman, J. N. Goldberg, A. P. Held) (to appear).

  44. Rawnsley, J. H.: On the Atiyah-Hitchin-Drinfeld-Manin vanishing theorem for cohomology groups of instanton bundles. Math. Ann.241, 43–56 (1979)

    Google Scholar 

  45. Serre, J-P.: Un théorème de dualité. Commun. Math. Helv.29, 9–26 (1955)

    Google Scholar 

  46. Siu, Y. T.: Analytic sheaf cohomology groups of dimension n of n-dimensional noncompact complex manifolds. Pac. J. Math.28, 407–411 (1969)

    Google Scholar 

  47. Swan, R. G.: The theory of sheaves. Chicago, London: University of Chicago Press 1964

    Google Scholar 

  48. Ward, R. S.: The twisted photon. Twistor Newsletter 1, 2–4 (1976)

    Google Scholar 

  49. Ward, R. S.: Curved twistor spaces. D. Phil. thesis, Oxford 1977

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

    Google Scholar 

  51. Ward, R. S.: Sheaf cohomology and an inverse twistor function. Twistor Newsletter6, 13–15 (1977)

    Google Scholar 

  52. Ward, R. S.: A class of self-dual solutions of Einstein's equations. Proc. R. Soc. London Ser. A363, 289–295 (1978)

    Google Scholar 

  53. Wells, R. O. Jr.: Differential analysis on complex manifolds. Berlin, Heidelberg, New York: Springer 1980

    Google Scholar 

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

    Google Scholar 

  55. Wells, R. O. Jr.: Cohomology and the Penrose transform. In: Complex manifold techniques in in theoretical physics (eds. D. E. Lerner, P. D. Sommers) Research Notes in Math.32, 92–114. San Fransisco, London, Melbourne: Pitman 1979

    Google Scholar 

  56. Wells, R. O., Jr.: Hyperfunction solutions of the zero-rest-mass field equations in Commun. Math. Phys. (to appear)

  57. Woodhouse, N. M. J.: Twistor cohomology without sheaves. In: Advances in twistor theory (eds. L. P. Hughston, R. S. Ward,) Research Notes in Math. 37. San Francisco, London, Melbourne: Pitman 1979

    Google Scholar 

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Communicated by A. Jaffe

Research supported by the National Science Foundation, the Institute for Advanced Study, and the Vaughn Foundation

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Eastwood, M.G., Penrose, R. & Wells, R.O. Cohomology and massless fields. Commun.Math. Phys. 78, 305–351 (1981). https://doi.org/10.1007/BF01942327

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