Spinors and Space-Time: Volume 1, Two-Spinor Calculus and Relativistic Fields
This 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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2-surface ABCD algebra anti-symmetric applied Argand plane basis bilinear transformation 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 timelike topological torsion totally reflexive transvecting unique unprimed valence vanish vector fields vector space world-tensor world-vector zero
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Symmetries and Curvature Structure in General Relativity
Graham S. Hall
No preview available - 2004