Given an arbitrary pseudo-Riemannian manifold M of dimension ( p , q ) , one may consider its tangent bundle T M . At any given point x ∈ ∈ M , the tangent space T x M is a ( p , q ) dimensional vector space. Given this vector space, one can construct the Clifford algebra C l ( p , q ) on it. If { e i } are a vector space basis on T x M , one may construct a pair of Weyl spinors as