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.