Physics – Mathematical Physics
Scientific paper
2010-04-28
Physics
Mathematical Physics
The curvature pieces of all wave equations exhibited in the paper had been rearranged before because of the question as to whe
Scientific paper
The classical two-component spinor formalisms for general relativity as built up by Infeld and van der Waerden afford an elegant approach to spacetime geometry. Deeply involved in the inner structure of these formalisms is the beautiful theory of spin densities of Schouten. In this review Schouten's theory is presented in detail. It is pointed out that spin affinities can most naively be introduced by carrying out parallel displacements of null world vectors. A complete algebraic description of spin curvatures is accomplished on the basis of the construction of a set of torsionless covariant commutators. It turns out that the implementation of such commutators under certain circumstances gives rise to a system of wave equations for gravitons and photons which possess a gauge-invariance property associated with appropriate spinor-index configurations. The situation regarding the derivation of the natural couplings between Dirac fields and spin curvatures is entertained.
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