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This present work is based on our previous publications, which all togethertrigger our "Killing spinor programme". Other significant spinor fields areinjected into the scheme and the intricate relations between them and theirbilinears are constructed here. The web of relations concerning theseconstructions are presented clearly in a Venn diagram. Particular attention isdevoted to the construction of equations satisfied by the homogeneous bilinearsinduced from Dirac spinors. Contacts with various physics theories are madethroughout the text and some of the future directions of the programme aredefined.

New Developments in Killing Spinor Programme and More Motivations for Physics