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