25: Spin, Spinors, and the Pauli Connection

We begin this chapter with a quotation: “No one fully understands spinors. Their algebra is formally understood but their general significance is mysterious. In some sense they describe the ‘square root’ of geometry and, just as understanding the square root of −1 took centuries, the same might be true of spinors.” The speaker, a mathematician of highest repute in many areas including the fields of particle physics and its relationships, shall be nameless, mainly because I seem to have mislaid the reference for this rather gloomy prognostication. Were he to become aware of it, I should hope he would forgive me for saying so, but I think we may be able to do better than that; I don’t think I can afford to wait centuries and perhaps the rest of this chapter will indicate why we don’t really need to…