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.