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An Introduction to Twistor Theory (London Mathematical Society Student Texts) Paperback – 21 Jul 1994

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' … the book is recommended to anyone seeking to get acquainted with the area.' American Scientist

' … a certain amount of preliminary knowledge is assumed of the reader ... but anyone who has these prerequisites and who is interested in twistor theory could hardly do better than to start with this book.' Contemporary Physics

'In all, the book provides a pleasant starting point for the study of this fascinating subject.' Dr F. E. Burstall, Contemporary Physics

Book Description

This text is an introduction to twistor theory and modern geometrical approaches to space-time structure at the graduate or advanced undergraduate level.

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Twistor Theory began as a subject in the late 1960's with the appearance of Penrose's two papers (1967,1968a). Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Amazon.com: 2 reviews
9 of 9 people found the following review helpful
Good introduction 10 April 2006
By Dean Welch - Published on Amazon.com
Format: Paperback
I think this book gives a very good introduction to twistor theory. However, it's not an elementary book. Readers should already be familiar with topology, differential geometry, group theory and general relativity. The book is short, as are the chapters, and it gets to the point quickly. I consider it primarily a math book, but aspects of physics are frequently considered.

After a quick introduction and review of tensors the concept of spinors is introduced. It's the usual approach drawing a correspondence between a vector and a rank (1,1) spinor. In particular between a null vector and the product of a spinor with its own conjugate. This is often informally phrased by saying a spinor is the square root of a vector.

Following this the spinor algebra is developed. At this point it is shown how to formulate tensor algebra in terms of spinors (with some bits of projective geometry thrown in). Although the book is developing the mathematics of spinors some familiarity with physics is required to appreciate all the discussion. Without some background in physics, relativity in particular, the significance of this might be missed. Applications considered include: Einstein's equation, the Weyl tensor, principle null directions and the classification of spacetime, Dirac neutrinos, source free Maxwell equations and congruences of null vectors. I would have like to have seen more discussion about the advantages of the spinor formulation, for example, how it makes classifying algebraically special spacetimes simpler.

Twistors are introduced next, this is about one-third of the way through the book. Although the correspondence between twistor space and null geodesics is considered; the original motivation of twistors, to provide a theory of quantum spacetime, isn't emphasized.

The rest of the book mainly contains chapters explaining various applications of twistor theory. They mostly have very physics sounding names like "The non-linear graviton" or "The twisted photon and Yang-Mills construction". My favorite chapter was the one covering Penrose's quasi-local momentum and quasi-local angular momentum. I may have missed something, but with the exception of this chapter I'm not sure any of the others offered any new insights to the world of physics.

On the whole I thought this was a very good book. I liked the pace and the text was clear. It even includes hints to some of the exercises. However, it does require a bit of background knowledge, I would especially recommend being familiar with topology. Obviously it's not as comprehensive as Penrose and Rindler or Ward and Wells, but it's very good for building a foundation.
... that they reveal clearly profound structure that is not easily noticed using other formalisms 21 Dec. 2014
By Jim Curry - Published on Amazon.com
Format: Paperback Verified Purchase
I believe that spinors and twistors are very important and that they reveal clearly profound structure that is not easily noticed using other formalisms. There can be no doubt that Sir Roger Penrose has been the leading exponent of this line of thinking for a long, long time. His book, Spinors and Spacetime is indispensable and a great classic, but it isn't always the easiest book to read. In particular, I've spent a lot of time sorting through his first chapter, trying to see clearly just what a spinor "really is." For me, at least, this little text by Huggett and Tod is the perfect jump start. It is, undeniably, terse, but that is actually helpful. It takes the shortest path in showing just what a spinor really is and how to work with it. A new reader might take half an hour or an hour to figure out the notes that go with a page of the writing, but it is clear, it conveys proper understanding, and gets to the point as efficiently as possible. In contrast, the first chapter of Spinors and Spacetime is very illuminating, but reads something like personal calculational notes. I find more insight from it after reading Huggett than before. I am convinced that this formalism is of such importance that it will come, in the fullness of time, to be a dominant language of mathematical physics. To many, it seems a bit abstract and unattractive. To me, it is the "right" language, and I need to speak it well, whether I start out finding it convenient or not. Huggett and Tod have done a great service. I don't know any other book that is very helpful to get a start in these matters. This one is helpful.
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