Geometry, Spinors, and Applications

This book is concerned with covariant and Lie differentiation of spinor fields, in the general context of not necessarily metric-compatible connections and non Killing-vector directions, respectively. Some earlier investigations of special cases are presented here in a unified fashion. New results are also established, which appear in print for the first time.
This work should be helpful to graduate students and researchers. Students can benefit from the introduction to aspects of algebra, geometry and spinors and their applications, whereas researchers may concentrate on the specific problem of spinorial differentiation.

• List of tables
• List of figures
• Preface
• I Preliminaries and Algebraic Aspects of Spinors 1
  1 General Vector Spaces 5
  2 Vector Spaces with a Metric 31
• II Preliminaries and geometrical aspects of spinors 71
  3 Manifolds in General 73
  4 Lie Groups as Special Manifolds 135
  5 Fibre Bundles as Special Manifolds 157
• III General Spinorial Differentiation 193
  6 Geometrical Definition of C[subscript 31](R) Spinors 197
  7 Differentiation of Spinor Fields 201
  8 Interplay between Differentiations 235
  9 The Invariant Formalism 255
• IV Illustrations and Applications 265
  10 Newtonian Mechanics and C[subscript 30](R) 269
  11 Electro-Magnetism 281
  12 Cartan Formalism 311
  13 Geometrical Gravitational Theories 317
• App. A Infeld-van der Waerden Symbols 347
• App. B Maxwell's Equations: Complements 353
• Bibliography 359
• Index 365