Spinors ? (Q1072111)

The author considers the question of the consistency of the notion of a spinor as it is widely understood and used in quantum gravity and quantum field theory. In effect he poses the following question: are there extensions of the definition of spinors which render them compatible with different pseudo-Riemannian metrics on a differentiable manifold ? The answer which he gives in detail is that there are no finite-dimensional true spinors compatible with the family of pseudo-Riemannian metrics on a smooth oriented manifold, i.e., in a broad sense spinors are really tensor fields.