Contact email: andrew[AT]synth.co.uk
my Main Page
There is much more about twistor theory in his enormous new book The Road to Reality (2004). This book also contains some last-minute passages with the first discussion of Witten's new work and its implications for twistor theory.
F. David Peat, Superstrings and the Search for the Theory of Everything (1988, paperback 1991) describes twistor theory, putting it in context by comparing and contrasting it with superstring theory. It is an enthusiastic if unreliable account.
For some mysterious technical reason the main index page is inaccessible but these very useful papers can still be reached:
Additionally, Stephen Huggett's lecture on The elements of twistor theory (2005) is available on-line here or here
There is much further material in
For an introduction to research in twistor theory, the best starting-point is the collection of papers in
The other point of view, more ambitious, is that of the twistor programme for physics, in which it is held that the usual description of space-time must be superseded by a grounding in some form of twistor geometry if the nature of the physical world is to be understood. It is in this spirit that I have pursued my own research.
Very roughly, attempts to implement the twistor programme have since 1970 branched into two directions. One is concerned with reformulating General Relativity, i.e. gravity, in terms of twistor geometry.
For a 1999 survey by Roger Penrose of this aspect of the programme, see this page from UC at Santa Barbara which has the 20 transparencies of Penrose's talk and an on-line Real Audio recording of the talk and discussion as well.
The other is about the twistor reformulation of Quantum Field Theory, i.e. the flat-space theory of elementary particles and forces. For the programme to be successful these directions must converge, and there are some exciting hints of a connection emerging. However, the research lines have been independent so far.
Within the latter of these two branches, there are again two main directions of enquiry which have been followed, complementary to each other. One is on the question of whether the spectrum of elementary particles — their masses, spins and other properties — can be understood within twistor geometry. This has so far largely been a study of twistor algebra.
The other line of investigation concentrates on the scattering amplitudes for elementary particles, and is largely a question of twistor integral calculus.
The calculus required turns out to be that of many-dimensional contour integrals of a very special form. They are very conveniently represented by a diagrammatic formalism which is a development of the original ideas introduced by Roger Penrose in 1970. My research concerns the connection between scattering amplitudes and these twistor diagrams.
Roughly speaking, twistor diagrams are the analogue of Feynman diagrams. Like Feynman diagrams, they are based on the idea of getting the amplitude for a physical process by expanding in increasing powers of the coupling constants. Whilst Feynman diagrams evaluate scattering amplitudes as the result of multiple integrations over space-time, twistor diagrams involve multiple integrals in twistor space.
However, at that point the similarities end and the differences begin.
To summarise: Feynman diagrams have the essential property of being derived from a generating principle (the Lagrangian). Their main problems arise from the fact that they do not as they stand give finite amplitudes.
In contrast, twistor diagrams are defined in such a way as to be manifestly finite. They are always compact contour integrals. Many particular twistor diagrams are now known to correspond to particular scattering processes. We do not yet know a generating principle from which these examples can all be derived. But new developments are making this look a much more realistic goal.
|
Twistor Diagrams Home Page Contact email: andrew[AT]synth.co.uk |
my Main Page |