## Spinors and Space-Time: Volume 1, Two-Spinor Calculus and Relativistic FieldsThis volume introduces and systematically develops the calculus of 2-spinors. This is the first detailed exposition of this technique which leads not only to a deeper understanding of the structure of space-time, but also provides shortcuts to some very tedious calculations. Many results are given here for the first time. |

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### Contents

The geometry of worldvectors and spinvectors | 1 |

12 Null directions and spin transformations | 8 |

13 Some properties of Lorentz transformations | 24 |

14 Null flags and spinvectors | 32 |

15 Spinorial objects and spin structure | 41 |

16 The geometry of spinor operations | 56 |

Abstract indices and spinor algebra | 68 |

22 The abstractindex formalism for tensor algebra | 76 |

49 Spinor form of commutators | 242 |

410 Spinor form of the Bianchi identity | 245 |

411 Curvature spinors and spincoefficients | 246 |

412 Compacted spincoefficient formalism | 250 |

413 Cartans method | 262 |

414 Applications to 2surfaces | 267 |

415 Spinweighted spherical harmonics | 285 |

Fields in spacetime | 312 |

23 Bases | 91 |

24 The total reflexivity of G on a manifold | 98 |

25 Spinor algebra | 103 |

Spinors and worldtensors | 116 |

32 Null flags and complex null vectors | 125 |

33 Symmetry operations | 132 |

34 Tensor representation of spinor operations | 147 |

35 Simple propositions about tensors and spinors at a point | 159 |

36 Lorentz transformations | 167 |

Differentiation and curvature | 179 |

42 Covariant derivative | 190 |

43 Connectionindependent derivatives | 201 |

44 Differentiation of spinors | 210 |

45 Differentiation of spinor components | 223 |

46 The curvature spinors | 231 |

47 Spinor formulation of the EinsteinCartanSciamaKibble theory | 237 |

48 The Weyl tensor and the BelRobinson tensor | 240 |

52 EinsteinMaxwell equations in spinor form | 325 |

53 The Rainich conditions | 328 |

54 Vector Bundles | 332 |

55 YangMills Fields | 342 |

56 Conformal rescalings | 352 |

57 Massless fields | 362 |

58 Consistency conditions | 366 |

59 Conformal invariance of various field quantities | 371 |

510 Exact sets of fields | 373 |

511 Initial data on a light cone | 385 |

512 Explicit field integrals | 393 |

diagrammatic notation | 424 |

435 | |

445 | |

457 | |

### Other editions - View all

Spinors and Space-Time: Volume 1, Two-Spinor Calculus and Relativistic Fields Roger Penrose,Wolfgang Rindler No preview available - 1984 |

Spinors and Space-Time: Volume 1, Two-Spinor Calculus and Relativistic Fields Roger Penrose,Wolfgang Rindler No preview available - 1984 |

### Common terms and phrases

2-surface ABCD algebra anti-symmetric applied Argand plane basis bundle commutator complex conjugate complex numbers components conformal weight conformally invariant consider contraction corresponding covariant derivative cross-ratio cross-sections curvature defined definition differential Dirac electromagnetic elements equivalent exact set example expression fact field equations flag plane flagpole follows formalism formulae gauge geometrical given identity index substitution indices light cone linear Lorentz transformation manifold massless metric Minkowski tetrad module multiplication notation Note null directions null flag null vectors obtain orthogonal outer multiplication outer product pair properties quantities relation rescaling restricted Lorentz result Riemann sphere rotation satisfies scalar fields simply skew space-time spacelike sphere spin transformation spin-coefficients spin-frame spin-vector spin-weighted spin-weighted spherical harmonics spinor form structure symmetric spinor tensor tensor algebra timelike topological torsion totally reflexive transvecting unique unprimed valence vanish vector fields vector space world-tensor world-vector zero