New Developments in Killing Spinor Programme and More Motivations for Physics

This present work is based on our previous publications, which all together trigger our “Killing spinor programme”. Other significant spinor fields are injected into the scheme and the intricate relations between them and their bilinears are constructed here. The web of relations concerning these constructions are presented clearly in a Venn diagram. Particular attention is devoted to the construction of equations satisfied by the homogeneous bilinears induced from Dirac spinors. Contacts with various physics theories are made throughout the text and some of the future directions of the programme are defined.