Geometry of curved space–times equipped with torsionful affinities and Einstein–Cartan’s theory in two-component spinor form

The classical world structures borne by space–times endowed with torsionful affinities are reviewed. Subsequently, the definition and symmetry properties of a typical pair of Witten curvature spinors for such space–times are exhibited along with a comprehensive two-component spinor transcription of Einstein–Cartan’s theory. A full description of the correspondence principle that interrelates Einstein–Cartan’s theory and general relativity is likewise presented.