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References
Comprehensive reviews of twistor theory appear in:Penrose, R. and Ward, R.S., “Twistors for Flat and Curved Spacetime” in General Relativity and Gravitation (ed. A. Held), Plenum, 1980; Hughston, L.P. and Ward, R.S., Advances in Twistor Theory, Pitman, 1979; Wells, R.O., Complex Geometry in Mathematical Physics, SMS #78, Les Presses de l'Univ. de Montreal, 1982; Penrose, R., and Rindler, W., Spinors and Space-time (2 volumes) Cambridge, 1984–1985; Hugget, S.A., and Tod, K.P., An Introduction to Twistor Theory, Cambridge, 1985.
For a discussion of CM, see Penrose and Rindler, ref. [1].
These spaces, as well as others which play an important role in the twistor programme, are all “flag manifolds” of T = C4. See Wells, R., Complex Geometry in Mathematical Physics, Les Presses de L'Universite de Montreal, 1982.
See references above, or Newman, E.T. and Hansen, R., Gen. Rel. Grav. 6, 361, 1975.
Ward, R., Phys. Lett. A61, 81, 1977.
Atiyah, M., and Ward, R., Comm. Math. Phys. 59, 117, 1977.
Atiyah, M.F., Drinfeld, V.G., Hitchin, N.Y., and Manin, Yu. I., Phys. Lett. A65, 185, 1978. Atiyah, M.F., Geometry of Yang-Mills Fields, Scuola Normale Superiore, 1979.
We refer especially to the work on “Fake Ros”. See Donaldson, S., J. Diff. Geom. 18, 269, 1983; and Freed, D., and Uhlenbeck, K., Instantons and Four-Manifolds, Springer, 1984.
Coleman, S., “The Uses of Instantons”, lecture notes from 1977 International School of Subnuclear Physics, 1977.
Isenberg, J., Yasskin, P.B., and Greep, P., Phys. Lett. 78B, 462, 1978. Isenberg, J. and Yasskin P.B., “Twistor Description of Non-Self-Dual Yang-Mills Fields”, in Complex Manifold Techniques in Theoretical Physics (eds. D. Lerner and P. Sommers), Pitman, 1979.
Witten, E., Phys. Lett. 77B, 394, 1978.
Witten, E., Nucl. Phys., B266, 245, 1986.
A “deformation” of a complex manifold may be understood as a smoothly parametrized set of transformations of the complex transition functions (on patch overlaps) which define the holomorphic structure of the manifold. The paramtrized set must include the identity transformation.
Penrose, R., Gen. Rel. Grav. 7, 31, 1976. Curtis, W.D., Lerner, P.F., and Miller, F.R., Gen. Rel. Grav. 10, 557, 1976. Hitchin, N.J., Math. Proc. Camb. Phil. Soc. 85, 465, 1979.
Yasskin, P.B., and Isenberg, J., Gen. Rel. Grav. 14, 621, 1982.
LeBrun, C., Trans AMS 278, 208, 1983. Eastwood, M., Twistor Newsletter 17, 1983. Basten, R., and Mason, L., Twistor Newsletter 21, 1986.
Isenberg, J., and Yasskin, P., Twistor Newsletter 22, 1986.
Unpublished.
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Shaw, W., Class and Qtm Grav 2, 113, 1985. Shaw, W., to appear in Mathematics in General Relativity, (ed., J. Isenberg) AMS Contemp Math.
It would be interesting if someone were to apply some of Segal's ideas on quantum field to the space of classical string field solutions which arises in Shaw's work. See Segal, I., J. Math. Phys. 1, 468, 1959.
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Isenberg, J. (1987). The ambitwistor program. In: de Vega, H.J., Sánchez, N. (eds) Field Theory, Quantum Gravity and Strings II. Lecture Notes in Physics, vol 280. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-17925-9_35
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DOI: https://doi.org/10.1007/3-540-17925-9_35
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