# 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.