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Twistor theory for LQG

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Post-edited
Authors : Eastwood, Michael (Author of the conference)
CIRM (Publisher )

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Symmetry in four dimensions Complex homogeneous spaces Twistors Bateman's formula Invariant differential operators Massless field equations Penrose transform Curved twistors Parabolic geometry
Abstract : Twistor Theory was proposed in the late 1960s by Roger Penrose as a potential geometric unification of general relativity and quantum mechanics. During the past 50 years, there have been many mathematical advances and achievements in twistor theory. In physics, however, there are aspirations yet to be realised. Twistor Theory and Loop Quantum Gravity (LQG) share a common background. Their aims are very much related. Is there more to it? This talk will sketch the geometry and symmetry behind twistor theory with the hope that links with LQG can be usefully strengthened. We believe there is something significant going on here: what could it be?

Keywords : twistor theory; conformal differential geometry; complex geometry

MSC Codes :
32L25 - Twistor theory, double fibrations
 53A30 - Conformal differential geometry
 53C28 - Twistor methods
    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 27/09/2019
    Conference Date : 02/09/2019
    Subseries : Research talks
    arXiv category : Differential Geometry
    Mathematical Area(s) : Algebraic & Complex Geometry ; Lie Theory and Generalizations ; Mathematical Physics
    Format : MP4 (.mp4) - HD
    Video Time : 00:45:47
    Targeted Audience : Researchers
    Download : 2019-009-02_eastwood.mp4
Information on the Event

Event Title : Twistors and Loops Meeting in Marseille / Théorie des twisteurs et gravitation quantique à boucles
Event Organizers : Dunajski, Maciej ; Rovelli, Carlo ; Speziale, Simone ; Vidotto, Francesca
Dates : 02/09/2019 - 06/09/2019
Event Year : 2019
Event URL : https://conferences.cirm-math.fr/2082.html

Citation Data

DOI : 10.24350/CIRM.V.19559703
Cite this video as: Eastwood, Michael (2019). Twistor theory for LQG. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19559703
URI : http://dx.doi.org/10.24350/CIRM.V.19559703

See Also

Bibliography

  • PENROSE, Roger. The apparent shape of a relativistically moving sphere. In : Mathematical Proceedings of the Cambridge Philosophical Society. Cambridge University Press, 1959. p. 137-139. - https://doi.org/10.1017/S0305004100033776

  • PENROSE, Roger. Twistor algebra. Journal of Mathematical physics, 1967, vol. 8, no 2, p. 345-366. - https://doi.org/10.1063/1.1705200

  • WOLF, Joseph A. The action of a real semisimple group on a complex flag manifold. I: Orbit structure and holomorphic arc components. Bulletin of the American Mathematical Society, 1969, vol. 75, no 6, p. 1121-1237. - https://doi.org/10.1090/S0002-9904-1969-12359-1

  • BATEMAN, Harry. The solution of partial differential equations by means of definite integrals. Proceedings of the London Mathematical Society, 1904, vol. 2, no 1, p. 451-458. - https://doi.org/10.1112/plms/s2-1.1.451

  • PENROSE, Roger. Solutions of the Zero‐Rest‐Mass Equations. Journal of mathematical Physics, 1969, vol. 10, no 1, p. 38-39. - https://doi.org/10.1063/1.1664756

  • ANDREOTTI, Aldo et NORGUET, François. La convexité holomorphe dans l'espace analytique des cycles d'une variété algébrique. Annali della Scuola Normale Superiore di Pisa-Classe di Scienze, 1967, vol. 21, no 1, p. 31-82. - http://www.numdam.org/item/ASNSP_1967_3_21_1_31_0/

  • SCHMID, Wilfried. Homogeneous complex manifolds and representations of semisimple Lie groups. Proceedings of the National Academy of Sciences of the United States of America, 1968, vol. 59, no 1, p. 56. - https://doi.org/10.1073/pnas.59.1.56

  • PENROSE, Roger. The nonlinear graviton. General Relativity and Gravitation, 1976, vol. 7, no 2, p. 171-176. - https://doi.org/10.1007/BF00763433

  • CARTAN, Elie. Les espaces à connexion conforme. Annales de la Société Polonaise de Mathématique, 1923, vol.2, p. 171-221. -

  • THOMAS, Tracy Yerkes. On conformal geometry. Proceedings of the National Academy of Sciences of the United States of America, 1926, vol. 12, no 5, p. 352. - https://doi.org/10.1073/pnas.12.5.352

  • FEFFERMAN, Charles. Parabolic invariant theory in complex analysis. Advances in Mathematics, 1979, vol. 31, no 2, p. 131-262. - https://doi.org/10.1016/0001-8708(79)90025-2

  • GRAHAM, C. Robin. Invariant theory of parabolic geometries. Lecture Notes in Pure and Appl. Math., 1993, vol. 143, p. 53-66. -


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