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Given a differentiable manifold with a tetrad of signature (p,q) over it (see tetrad for notation and prelimenaries), 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 SO(p,q) ). Actually, when p+q <= 3, we can have more interesting bundles like anyonic bundles!
Spinor bundles inherit a connection from a connection on the vector bundle V (see tetrad).
See also associated bundle.
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