31. The above can be generalized for vector fields, tensor fields, and spinor fields. 32. The number of supercharges in a spinor depends on the dimension and the signature of spacetime. 33. They are a special kind of spinor field related to Killing vector fields and Killing tensors. 34. Therefore, these constitute a third kind of quantity, which is known as a spinor . 35. Where \ nabla _ \ mu is the general-relativistic covariant derivative of a spinor . 36. In 1947 Marcel Riesz constructed spinor spaces as elements of a minimal left ideal of Clifford algebras. 37. Thus a spinor may be viewed as an isotropic vector, along with a choice of sign. 38. This is mathematically contained in the spinor fields which are the solutions of the relativistic wave equations. 39. The' ) spins, and spinor representations for fermions with their half-integer spins. 40. This latter approach has the advantage of providing a concrete and elementary description of what a spinor is.
