## Twistor Geometry and Field TheoryThis book deals with the twistor treatment of certain linear and non-linear partial differential equations in mathematical physics. The description in terms of twistors involves algebraic and differential geometry, and several complex variables, and results in a different kind of setting that gives a new perspective on the properties of space-time and field theories. The book is designed to be used by mathematicians and physicists and so the authors have made it reasonably self-contained. The first part contains a development of the necessary mathematical background. In the second part, Yang-Mills fields and gravitational fields (the basic fields of contemporary physics) are described at the classical level. In the final part, the mathematics and physics are married to solve a number of field-theoretical problems. |

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### Contents

II | 1 |

III | 5 |

IV | 7 |

V | 19 |

VI | 26 |

VII | 28 |

VIII | 36 |

IX | 45 |

XXVIII | 264 |

XXIX | 270 |

XXX | 279 |

XXXI | 286 |

XXXIII | 293 |

XXXIV | 301 |

XXXV | 303 |

XXXVI | 325 |

### Common terms and phrases

ansatz anti-self-dual Chern coefficients cohomology groups complex manifold complex vector complexification connection consider coordinate chart corresponding curvature curves define denote differential forms dimension Dirac discussed double fibration dual element equivalent exact sequence example Exercises for Section fiber field equations field theory follows frame gauge field gauge group geometry given global helicity hence Hermitian holomorphic functions holomorphic vector bundle homogeneous homology hyperfunction induced instantons integral isomorphism Lemma Lie group line bundle linear mapping massless field matrix Maxwell metric Minkowski space module notation null lines one-form open set parameters Penrose transform positive-definite principal bundle proof pullback recall restriction Rham satisfying scalar self-dual sheaf cohomology sheaves Show smooth solutions space-time spectral sequence spin structure spinor bundles spinor field submanifold subspace tangent bundle tensor Theorem tion topological transition functions trivial twistor space two-form vanishes vector fields vector space well-defined Yang-Mills zero