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
on the space of spinors
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.
The spinor bundle
is defined [1] to be the complex vector bundle
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.