The Classical Two-Component Spinor Formalisms for General Relativity I

摘要

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 frameworks is the beautiful theory of spin densities of Schouten. In this work Schouten's theory is presented in detail. The elementary aspects of the spin-affine geometry borne by the formalisms are then described in a systematic way. It is particularly shown that the symmetric parts of any admissible spin connections behave covariantly under the action of the Weyl gauge group.