Spinor Bundle

Given a differentiable manifold M with a tetrad of signature (p,q) over it, a spinor bundle over M is a vector SO(p,q)-bundle over M such that its fiber is a spinor representation of
Spin(p,q),
the double cover of the special orthogonal group SO(p,q). Spinor bundles inherit a connection from a connection on the vector bundle V (see tetrad). When
p + q ≤ 3
there are some further possibilities for covering groups of the orthogonal group, so other bundles (anyonic bundles). See also associated bundle.
     

 

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