An Introduction to Twistor Theory (London Mathematical Society Student Texts, Series Number 4)

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. Contents......Page 7 Preface......Page 9 Preface to the second edition......Page 11 1 Introduction......Page 13 2 Review of Tensor Algebra and Calculus......Page 17 3 Lorentzian Spinors at a Point......Page 23 4 Spinor Fields......Page 37 5 Compactified Minkowski Space......Page 45 6 The Geometry of Null Congruences......Page 57 7 The Geometry of Twistor Space......Page 65 8 Solving the Zero Rest Mass Equations I......Page 77 9 Sheaf Cohomology and Free Fields......Page 83 10 Solving the Zero Rest Mass Equations II......Page 103 11 The Twisted Photon and Yang-Mills Constructions......Page 111 12 The Non-Linear Graviton......Page 117 13 Penrose's Quasi-Local Momentum and AngularMomentum......Page 131 14 Functionals on Zero Rest Mass Fields......Page 149 15 Further Developments and Conclusions......Page 159 16 Hints, Solutions and Notes to the Exercises......Page 165 Appendix: The GHP Equations......Page 175 Bibliography......Page 179 Index......Page 187 This book is an introduction to twistor theory and modern geometrical approaches to space-time structure at the graduate or advanced undergraduate level. The choice of material presented has evolved from graduate lectures given in London and Oxford and the authors have aimed to retain the informal tone of those lectures. The book will provide graduate students with an introduction to the literature of twistor theory, presupposing some knowledge of special relativity and differential geometry. It would also be of use for a short course on space-time structure independently of twistor theory. The physicist could be introduced gently to some of the mathematics which has proved useful in these areas, and the mathematician could be shown where sheaf cohomology and complex manifold theory can be used in physics. This book is an introduction to twistor theory and modern geometrical approaches to space-time structure at the graduate or advanced undergraduate level. The choice of material presented has evolved from graduate lectures given in London and Oxford and the authors have aimed to retain the informal tone of those lectures.The book will provide graduate students with an introduction to the literature of twistor theory, presupposing some knowledge of special relativity and differential geometry. It would also be of use for a short course on space-time structure independently of twistor theory. The physicist could be introduced gently to some of the mathematics that has proved useful in these areas, and the mathematician could be shown where sheaf cohomology and complex manifold theory can be used in physics. Publisher Description (unedited publisher data) This book is an introduction to twistor theory and modern geometrical approaches to space-time structure at the graduate or advanced undergraduate level. It will be valuable also to the physicist as an introduction to some of the mathematics that has proved useful in these areas, and to the mathematician as an example of where sheaf cohomology and complex manifold theory can be used in physics Evolving From Graduate Lectures Given In London And Oxford, This Introduction To Twistor Theory And Modern Geometrical Approaches To Space-time Structure Will Provide Graduate Students With The Basics Of Twistor Theory, Presupposing Some Knowledge Of Special Relativity And Differenttial Geometry.