TWISTOR GEOMETRY, SPINOR STRUCTURE AND NATURE OF SUPERSPACE

Abstract

The nature of superspace is studied here from the viewpoint of eight-component conformal spinors which can be split into two Cartan semispinors having two internal helicities corresponding to particle and anti-particle states. This leads to the generation of internal symmetry through reflection group. It is shown that each member of the doublet can be taken to behave as twistors in complexified Minkowski space-time. This helps us to introduce a spinor structure at each space-time point and the spinor coordinate gives rise to the internal helicity. This may be achieved through the introduction of a direction vector attached to each space-time point. Superspace here appears as a bundle space where the base space is the ordinary Minkowski space-time and the spinorial coordinates generated through the introduction of the direction vector from the fibre. This suggests that the internal space of hadrons is anisotropic in nature.