An Introduction to Twistor TheoryThis 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. |
Contents
Introduction | 1 |
Review of Tensor Algebra and Calculus | 5 |
Lorentzian Spinors at a Point | 11 |
Spinor Fields | 25 |
Compactified Minkowski Space | 33 |
The Geometry of Null Congruences | 45 |
The Geometry of Twistor Space | 53 |
Solving the Zero Rest Mass Equations I | 65 |
Solving the Zero Rest Mass Equations II | 91 |
The Twisted Photon and YangMills Constructions | 99 |
The NonLinear Graviton | 105 |
Penroses QuasiLocal Momentum and Angular Momentum | 119 |
Functionals on Zero Rest Mass Fields | 137 |
Further Developments and Conclusions | 147 |
The GHP Equations | 163 |
Sheaf Cohomology and Free Fields | 71 |
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Common terms and phrases
a-plane Baston bivector Čech Čech cohomology chapter coboundary cocycle cohomology groups complex manifold conformal group conformal metric congruence consider constant construction contour integral coordinates corresponding CP¹ curvature curves define definition deformation Dolbeault Dolbeault cohomology dyad Eastwood equivalent exercise field equations flat space function elements geometry given H¹(X Hermitian homogeneous of degree Hughston infinity intersection isomorphism line bundle linearised Lorentz matrix Minkowski space momentum null cone null geodesics null vector paß Penrose plane quasi-local mass Riemann rotation satisfying scalar sheaf cohomology sheaves short exact sequence Show sin² solutions space-time sphere spinor field symmetric tangent tetrad Theorem time-like topological transformation twistor diagrams twistor equation twistor function twistor space twistor theory two-surface twistor U₁ vanishes vector field vector space Ward Weyl tensor Yang-Mills z.r.m. field zero rest mass