New Developments in Killing Spinor Programme and More Motivations for Physics

TL;DR

This paper advances the Killing spinor programme by exploring relations between spinor fields and their bilinears, connecting mathematical structures to physical theories and proposing future research directions.

Contribution

It introduces new spinor fields into the Killing spinor scheme and elucidates their relations and equations, enriching the mathematical framework and physical motivations.

Findings

Relations between spinor fields and bilinears are systematically constructed.

A Venn diagram illustrates the web of relations among these structures.

Connections to various physics theories are established.

Abstract

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.