Introduction to 2-spinors in General Relativity
World Scientific, 2003 - 204 páginas
This book deals with 2-spinors in general relativity, beginning by developing spinors in a geometrical way rather than using representation theory, which can be a little abstract. This gives the reader greater physical intuition into the way in which spinors behave. The book concentrates on the algebra and calculus of spinors connected with curved space-time. Many of the well-known tensor fields in general relativity are shown to have spinor counterparts. An analysis of the Lanczos spinor concludes the book, and some of the techniques so far encountered are applied to this. Exercises play an important role throughout and are given at the end of each chapter. Sample Chapter(s). Spinor Geometry (238 KB). Contents: Spinor Geometry; Spinor Algebra; Spinor Analysis; Lanczos Spinor. Readership: Postgraduate level students and researchers.
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algebraically arbitrary Bianchi identities brº Cabcd called Christoffel symbols coefficients transform commutation complex conjugate consider constant contraction covariant derivative covariant vector denoted dyad Einstein expression field equations geodesic coordinate system geometry given gravitational field Habe Hence independent components indices intrinsic derivatives Lanczos coefficients Lanczos tensor linear Lorentz matrix metric tensor Minkowski space natural basis Newtonian null cone null tetrad null tetrad transforms null vectors obtained parameter partial derivatives particle Penrose Petrov type principal null directions Rabcd Ricci tensor Riemann tensor rotation scalar field scalar quantity skew-symmetric space-time manifold spin basis transforms spin coefficients spin-vector spinor equivalent symmetric symmetry properties tensor field theorem theory timelike vector transformation law Transvecting unique tensor univalent spinor valence vector field vector space WABCD Weyl spinor Weyl tensor Weyl-Lanczos equations world-tensor write yields zero