Spinor bundle

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.