Geometric interpretation of the Pauli spinor

Abstract

We re-examine an intuitively geometric view of the nonrelativistic Pauli spinor and extend it to show how the abstract undotted and dotted spinors of SU(2) can be interpreted in terms of the homogeneous complex coordinates of various points in a stereographic projection plane. A simplified discussion of the connection between the rotation group and special transformations (elliptic homographies) in the plane of projection is presented. Finally, we relate this view of the spinor to those based on the existence of an isotropic or null vector.