TWISTOR DIAGRAMS

Website by
Andrew Hodges

Contact: Dr Andrew Hodges, Wadham College, Oxford University,
Parks Road, Oxford OX1 3PN, UK.
Email: andrew.hodges(AT)wadh.ox.ac.uk

Academic webpage at Wadham College
Personal webpage



August 2006. Photo by Colin Watson


Overview

TWISTOR theory is the creation of the great British mathematician and physicist, Professor Sir Roger Penrose, FRS, OM. The idea of twistor theory is that space and time should be described in a completely new way using the geometry of twistor space. Then fundamental physics should be reformulated in twistor geometry. The hope is that our puzzles with gravity and quantum mechanics can be resolved in this new framework.

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 doing some pretty difficult mathematics in many-dimensional-spaces. But they have a strange and beautiful structure which brings out some amazing properties of these interactions.

All this work went rather slowly 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 an new paper which related string theory and twistor geometry. People working in more orthodox research in physics suddenly started taking an interest in twistor geometry.

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, puts a rather different point of view.

What is sometimes called 'the twistor revolution' also meant that I learnt about the wonderful new discoveries that leading quantum field theorists were making in gauge theory, which is essentially the study of fundamental forces in Nature. These turned out to be closely connected with my efforts with twistor diagrams. My first main contribution was showing in 2005 that a development which had been inspired by Witten's paper (the 'Britto-Cachazo-Feng-Witten recursion relation'), was in fact best represented in terms of twistor diagrams. In March 2009, Nima Arkani-Hamed, Freddy Cachazo, Clifford Cheung, and Jared Kaplan published a paper on The S-matrix in Twistor Space, available here, made this idea much better known.

In 2009 I realised that another new development ('dual conformal invariance') could also be related to twistor diagram structure. This enabled me to make a good start on resolving one of the outstanding puzzles left by the BCFW recursion relation. My new paper Eliminating spurious poles from gauge theoretic amplitudes appeared on 11 May 2009 and is available here.

There is now a very wide field open for research, with a new generation of young physicists involved, and I have good hopes of major new developments before long.

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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
my Main Page


You can also listen to TWISTOR music by Matthew Hogan.