Description
Book SynopsisThis text is a self-contained, comprehensive treatment of the tensor and spinor calculus of space-time manifolds with as few technicalities as correct treatment allows. Both the physical and geometrical motivation of all concepts are discussed, helping the reader to go through the technical details in a confident manner. Several physical theories are discussed and developed beyond standard treatment using results in the book. Both the traditional "index" and modern "coordinate-free" notations are used side-by-side in the book, making it accessible to beginner graduate students in mathematics and physics. The methods developed offer new insights into standard areas of physics, such as classical mechanics or electromagnetism, and takes readers to the frontiers of knowledge of spinor calculus.
Table of ContentsPreface.-
Part I Preliminaries and Algebraic Aspects of Spinors: General Vector Spaces. Vector Spaces with a Metric.-
Part II Preliminaries and Geometrical Aspects of Spinors: Manifolds in General. Lie Groups as Special Manifolds. Fibre Bundles as Special Manifolds.-
Part III General Spinorial Differentiation: Geometrical Definition of
C31 (
R) Spinors. Differentiation of Spinor Fields. Interplay between Differentiations. The Invariant Formalism.-
Part IV Illustrations and Applications: Newtonian Mechanics and
C30 (
R). Electro-Magnetism. Cartan Formalism. Geometrical Gravitational Theories.- A: Infeld-van der Waerden Symbols.- B: Maxwells's Equations: Complements.
