In differential geometry, given a spin structure-dimensional orientable Riemannian manifold one defines the spinor bundle to be the complex vector bundle associated to the corresponding principal 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.

Formal definition

be a spin structure on a Riemannian manifoldthat is, an equivariant lift of the oriented orthonormal frame bundle of the special orthogonal group by the spin group.

The spinor bundle is defined 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

See also

• Clifford bundle

• Clifford module bundle

• Orthonormal frame bundle

• Spin geometry

• Spinor

• Spinor representation

Notes

Further reading

|