Geometrical Construction of Supertwistor Theory

Abstract

Supertwistor theory is geometrically constructed based on the SUSY Hopf map. We derive a new incidence relation for the geometrical supertwistor theory. The present supertwistor exhibits remarkable properties: Minkowski space need not be complexified to introduce spin degrees of freedom, and even number SUSY is {automatically} incorporated by the geometrical set-up. We also develop a theory for massless free particle in Minkowski superspace, which physically corresponds to the geometrical supertwistor theory. The spin degrees of freedom are originated from fermionic momenta as well as fermionic coordinates. The geometrical supertwistor is quantized to reproduce same physical contents as in the original supertwistor theory. Relationships to superspin formalism and SUSY quantum Hall effect are also discussed.