TWISTOR DIAGRAMSWebsite by
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 August 2006. Photo by Colin Watson |
My work is concerned mostly with the quantum mechanics side of this programme. Twistor diagrams, which Roger Penrose first wrote down in about 1970, give a description of how fundamental particles and forces act on each other. Twistor diagrams involve difficult mathematics in many-dimensional spaces. But from the start it became clear that they manifest a strange and beautiful structure which brings out some amazing properties of fundamental interactions.
Work on twistor diagrams made slow progress for thirty years, plagued by mathematical difficulties, and seemed rather far away from mainstream developments in physics. But in 2003 the leading theoretical physicist Edward Witten came up with a new paper which related string theory and twistor geometry. People working in more orthodox research in physics suddenly started taking an interest in twistors.
An article in the Guardian newspaper gave an impression of what is involved in this convergence of string theory, field theory and twistor theory. An article by Roger Penrose in New Scientist, July 2004, put his own point of view.
Quantum field theorists began talking about 'the twistor revolution'. And twistor theorists like myself started catching up with the wonderful discoveries that leading quantum field theorists had been making in gauge theory, which is essentially the study of fundamental forces in Nature.
My main contribution was showing in 2005 that one of these discoveries (the 'Britto-Cachazo-Feng-Witten recursion relation' for gauge theory), was in fact best represented in terms of twistor diagrams. This came as a rather an unexpected and surprising idea, and took some time to be absorbed.
In March 2009, Nima Arkani-Hamed, Freddy Cachazo, Clifford Cheung, and Jared Kaplan published a paper (The S-matrix in Twistor Space), which extended this idea from a new point of view and made it much better known. My Oxford colleagues David Skinner and Lionel Mason did parallel work.
In May 2009 I noticed that another new field-theoretic development ('dual conformal invariance') could also naturally be described using twistor diagram structure. This has also proved helpful, but it is only one component of the many further advances made in the summer of 2009 by Nima Arkani-Hamed's group, by my Oxford colleagues, and by other leading field theorists.
By September 2009, the basic idea of Roger Penrose's twistor-geometric approach had been firmly established.
The next stage requires the extension of these ideas to encompass the 'loop amplitudes' of quantum field theory, to make the right connection with gravity, and to establish a fundamental twistor-geometric dynamic principle. There is now a new generation of young mathematicians and physicists involved, and I have great confidence that the recent fast pace of progress will now be sustained. | 
Nima Arkani-Hamed and Roger Penrose meet at the White Hart, Wytham, Oxford, 18 June 2009. (Photo by AH). |
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I also have another area of research and publication: the history and philosophy of computing, stemming from my biography of Alan Turing. See my Turing Publications page. Technically, this is quite separate from my work in twistor theory, but there is an underlying connection because of my interest in Roger Penrose's theory of uncomputability in physics.
Contact email: andrew.hodges(AT)wadh.ox.ac.uk |
Turing publications |
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