Spinor bundle

In differential geometry, given a spin structure on an

-dimensional orientable Riemannian manifold

one defines the spinor bundle to be the complex vector bundle

and the spin representation of its structure group

A section of the spinor bundle

is called a spinor field.

be a spin structure on a Riemannian manifold

that is, an equivariant lift of the oriented orthonormal frame bundle

with respect to the double covering

of the special orthogonal group by the spin group.

is defined [1] to be the complex vector bundle

associated to the spin structure

via the spin representation

denotes the group of unitary operators acting on a Hilbert space

is a faithful and unitary representation of the group

[2] | This differential geometry-related article is a stub.